Second Quarter Group F Math Peta - Special Products (Sq. of Bi, Sq. of Tri, SDTT, Bi-Tri, Cu. of Bi)

SECOND QUARTER’s PERFORMANCE TASK:SPECIAL PRODUCTSICL: Showcase of Solution and Final Answer

Group Name: Factoring

Second Quarter Grade 8 Mathematics Performance Task Special Products 2

JUSTIN BACON

RAFAEL BIAG

DANIEL PAUL PEREZ

Justin Bacon


Insert Picture Here

Square of a Binomial

Product of SDTT

Square of Trinomial

Product of a Binomial & a Trinomial

Cube of a Binomial

Name:SQUARE OF A BINOMIAL● EASY QUESTION:

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Square of a

Binomial

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Trinomial

Product of SDTT

Product of a

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Second Quarter Grade 8 Mathematics Performance Task Special Products

4

Name:SQUARE OF A BINOMIAL● AVERAGE QUESTION:

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Square of a

Binomial

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Product of SDTT

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Name:SQUARE OF A BINOMIAL● CHALLENGING QUESTION:

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6

Dale drew a square with a side of (2x+1). Calculate for the area of the square.

Given: (2x+1) Formula: s^2 (Perform Square of a Binomial)Solution: (2x+1)^2 (2x)^2+2(2x)(1)+(1)^2 Final Answer: 4x^2+4x+1

Name:Product of Sum and Difference of Two Terms

● EASY QUESTION:

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● AVERAGE QUESTION:

Square of a

Binomial

Square of a

Trinomial

Product of SDTT

Product of a

Binomial and a

Trinomial

Cube of a Binomial

E A CSecond Quarter Grade 8 Mathematics Performance Task Special Products

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● CHALLENGING QUESTION:

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Given: [7+(x+y)][7-(x+y)]

Solution:1. 7^2= 492. + (x+y)^2= x^2+2xy+y^2

Final Answer: 49+x^2+2xy+y^2

Name:SQUARE OF A TRINOMIAL● EASY QUESTION:

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Name:SQUARE OF A TRINOMIAL● AVERAGE QUESTION:

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Name:SQUARE OF A TRINOMIAL● CHALLENGING QUESTION:

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Name:PRODUCT OF A BINOMIAL AND A TRINOMIAL

● EASY QUESTION:

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● AVERAGE QUESTION:

Square of a

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Square of a

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Binomial and a

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Cube of a Binomial


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● CHALLENGING QUESTION:

Square of a

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Name:CUBE OF A BINOMIAL● EASY QUESTION:

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Name:CUBE OF A BINOMIAL● AVERAGE QUESTION:

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Name:CUBE OF A BINOMIAL● CHALLENGING QUESTION:

Square of a

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Rafael Biag


Insert Picture Here


Product of SDTT

Square of Trinomial


Cube of a Binomial

Name:SQUARE OF A BINOMIAL○ EASY QUESTION:(y+ x)2 = y2 + 2yx + x2

1. The square of the first term of the binomial: y2

2. Twice the product of the two terms: 2yx3. The square of the second term: x2

FINAL ANSWER:y2 + 2yx + x2

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Name:SQUARE OF A BINOMIAL○ AVERAGE QUESTIOn (6x2 + 5a)2 ○ SOLUTION:

(6x2)2 + 2(6x2) (5a)+ (5a)2 36x4 +60x2a +25a21. The square of the first term of the binomial2. Twice the product of the two terms3. The square of the second term○○○○○○○

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Name:SQUARE OF A BINOMIAL○ CHALLENGING QUESTION:(11n + 10m2)2○ SOLUTION:○ = (11n)2 +2(11n)(10m)+(10m2)2 = 121n2

+220nm+100m 1. The square of the first term of the binomial2. Twice the product of the two terms3. The square of the second term○○○

○○○○○○○○

○○○

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Name:Product of Sum and Difference of Two Terms○ EASY QUESTION:(y – 4)(y + 4)

1. The First term (y) squared is y2.2. The second term will always be negative, and a perfect

square like the first term: (–4)(+4) = –16

FINAL ANSWER:

y2 - 16

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Name:Product of Sum and Difference of Two Terms○ AVERAGE QUESTION:(xy – 5)(xy+ 5)○ SOLUTION:1. The square of xy = (xy)2 = x2 y22. The second term is negative, and a perfect square like the

first term: 5 = –25.

FINAL ANSWER:

x2 y2 - 25

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Name:Product of Sum and Difference of Two Terms○ CHALLENGING QUESTION:5 + (b – a)][5 – (b– a)]○SOLUTION:

1. The square of 5 = 252. The second term is negative, and a perfect square like the first term:

(b - a) = - (b - a)23. Square the binomial and distribute the negative sign, which looks like this:

- (b2 - 2ba + a2) = - b2 + 2ba - a2

FINAL ANSWER:

25 - b2 + 2ba - a2

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Name:SQUARE OF A TRINOMIAL○ EASY QUESTION:6x2 - x - 2

find two numbers whose sum is the coefficient of the second term and whose product is equal to the product of the third term and the coefficient of the first term ( (6)(-2) or -12). By inspection, the desired numbers are found to be -4 and +3. Using these two numbers as coefficients for x, we can rewrite the original expression as 6x2 - 4x + 3x - 2

FINAL ANSWER:

(2x + 1)(3x - 2)

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Name:SQUARE OF A TRINOMIAL○ AVERAGE QUESTION:16x2 - 8xy + y2

To factor the trinomial, we simply take the square roots of the end terms and join them with a plus sign if the middle term is preceded by a plus or with a minus if the middle term is preceded by a minus.

FINAL ANSWER:

(4x - y)2

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Name:SQUARE OF A TRINOMIAL○ CHALLENGING QUESTION:

(0.5y²+1.2x²+1.5)²○SOLUTION:

○(0.5y²)²+(1.2x²)²+(1.5)²+2(0.5y²)(1.2x²)+2(0.5y²)(1.5)+2(1.2x²)(1.5)

FINAL ANSWER:0.25Y⁴+1.44X⁴+2.25²+1.2Y²X²+1.5Y²+3.6X²

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Name:PRODUCT OF A BINOMIAL AND A TRINOMIAL○ EASY QUESTION:(x−1)(x2−2x+1)○ SOLUTION:○ (x−1)(x2−2x+1)=x(x2−2x+1)−1(x2−2x+1)=x3−2x2+x−x2+2x−1

FINAL ANSWER:x3−3x2+3x−1

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Name:PRODUCT OF A BINOMIAL AND A TRINOMIAL○ AVERAGE QUESTION:(2x + y)(4x^2 - 2xy + 4y^2)

FINAL ANSWER:8^3 + y^3

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Name:PRODUCT OF A BINOMIAL AND A TRINOMIAL○ CHALLENGING QUESTION:(a + b)(a - ab + b^2)

FINAL ANSWER: a^3 + b^3

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Name:CUBE OF A BINOMIAL○ EASY QUESTION:(a + b)3

○SOLUTION:

○= a3 + 3a2b + 3ab2 + b3

FINAL ANSWER:

= a3 + 3ab (a + b) + b3

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Name:CUBE OF A BINOMIAL○ AVERAGE QUESTION:(2 – 3x)3 – (5 + 3x)3

○ SOLUTION:○ = {23 - 3.22.(3x) + 3.2.(3x)2 - (3x)3} – {53 + 3.52.(3x) + 3.5.(3x)2 + (3x)3}○ = {8 – 36x + 54 x2 - 27 x3} – {125 + 225x + 135x2 + 27 x3}○ = 8 – 36x + 54 x2 - 27 x3 – 125 - 225x - 135x2 - 27 x3

○ = 8 – 125 – 36x - 225x + 54 x2 - 135x2 - 27 x3 - 27 x3

○ = -117 – 261x - 81 x2 - 54 x3

FINAL ANSWER:

-117 – 261x - 81 x2 - 54 x3

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Name:CUBE OF A BINOMIAL○ CHALLENGING QUESTION:(5m + 2n)3 - (5m – 2n)3

○ SOLUTION:= {(5m)3 + 3.(5m)2. (2n) + 3. (5m). (2n)2 + (2n)3} – {(5m)3 - 3.(5m)2. (2n) + 3. (5m). (2n)2 - (2n)3}= {125 m3 + 150 m2 n + 60 m n2 + 8 n3} – {125 m3 - 150 m2 n + 60 m n2 - 8 n3}= 125 m3 + 150 m2 n + 60 m n2 + 8 n3 – 125 m3 + 150 m2 n - 60 m n2 + 8 n3

= 125 m3 – 125 m3 + 150 m2 n + 150 m2 n + 60 m n2 - 60 m n2 + 8 n3 + 8 n3

= 300 m2 n + 16 n3

FINAL ANSWER:

300 m2 n + 16 n3

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DANIEL PAUL PEREZ


Insert Picture Here


Product of SDTT

Square of Trinomial


Cube of a Binomial

(x+6)2=x2+12x+36 x2 is the square of x.12x is twice the product of x with 6. (x· 6 = 6x. Twice that is 12x.)36 is the square of 6.x2 + 12x + 36 is called a perfect square trinomial -- which is the square of a binomial.answer:x2+12x+36

DANIEL PAUL PEREZSQUARE OF A BINOMIAL

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E A CSecond Quarter Grade 8 Mathematics Performance Task Special Products 36

∗AVERAGE QUESTION: (5x3 − 1)2 =25x6 − 10x3 + 125x6 is the square of 5x3

−10x3 is twice the product of 5x3 and −1. (5x3 times −1 = −5x3. Twice that is −10x3.)1 is t.he square of −1answer:25x6 − 10x3 + 1

DANIEL PAUL PEREZSQUARE OF A BINOMIAL

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∗CHALLENGING QUESTION:(8x – 7y)2

we need to square the first term the first term is 64x^2 then twice the product of the first and the second terms 112xy then

square the last term 49y^2

solution:(8x-7y)^2(8x-7y)^2

answer:64x^2-112xy+49y^2

Name:SQUARE OF A BINOMIAL

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∗EASY QUESTION:(x+5)(x+5)To answer this we need to square the x and square the 5 or time the two term like 5 times 5 and x times xsolution:(x)2-(5)2

answer: x2-25

DANIEL PAUL PEREZProduct of Sum and Difference of Two

Terms

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∗AVERAGE QUESTION:(9x + 5) (9x - 5)∗= (9x)2 - (5)2∗= 81x2 - 25 ∗we going to multiply 9x9 the answer is 81 then x

times x will get x2∗5x5 will get 25answer:81x2-25

DANIEL PAUL PEREZProduct of Sum and Difference of Two Terms

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∗CHALLENGING QUESTION: (40 + 3)( 40 – 3)∗(40)2 – (3)2

∗1600 – 9to get the 40 we need to square it and 3 so i square the 40 i get 1600 then i square 3 i get 9

answer:1600-9

DANIEL PAUL PEREZProduct of Sum and Difference of Two

Terms

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∗EASY QUESTION: (x+6x+9x)2

To answer this we need to square the first square the second square the third twice the product of the first and the second twice the product of the first and the third twice the product of the second and the thirdsolution:(x)2+(6x)2+(9x)2+2(x)(6x)+2(x)(9x)+2(6x)(9x)answer:x2+36x2+81x2+36xx+18xx+108xx

DANIEL PAUL PEREZSQUARE OF A TRINOMIAL

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∗AVERAGE QUESTION: (5x + 3/2 y + z)2

to get the answer we need to square the first term then square the second term then square the third term then square the

first and the second then square the first and the third then the last to square is the second and the third

answer: 25x2 + 4/9 y2 + z2 + 15xy + 3yz + 10zx


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∗CHALLENGING QUESTION:∗ (1/9 a – 1/3 b + 10)2

to get the answer we need to square the first term then square the second term then square the third term then square the

first and the second then square the first and the third then the last to square is the second and the third

answer:1/81 a2 + 1/9 b2 + 100 – 2/27ab – 20/3b + 20/9a


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∗EASY QUESTION:(4a2-b3)(16a4+4a2b3+b6) to get the answer we need to cuben 4a^2 then cube the second the b^3 then cube it solution:(4a^2)^3-(b^3)^3

answer:64a^6-b^9

DANIEL PAUL PEREZPRODUCT OF A BINOMIAL AND A

TRINOMIAL

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∗AVERAGE QUESTION:(6r^3a-7t^2b)(36r^6a+42r^3at^2b+49t^4b)

like what we do we need to cube the (6r^3a)^3 then we need to cube the second (7+^2b)^3solution:(6r^3a)^3-(7+^2b)^3

answer:216^9a-343+^6b


TRINOMIAL

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∗CHALLENGING QUESTION:(2/3g^2+4/5h)(4/9g^4-8/15g^2h+16/25h^2

like what we did but this question we need to cross out something in the first (2/3g^2)^3 we need to cross out the two three then the second we dont cross them just cube them (4/5h)^3solution:(2/3g^2)^3+(4/5h)^3

answer:8/27g^6+64/125h^3


TRINOMIAL

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∗EASY QUESTION: (x + 5y)3 The sum of a cubed of two binomial is equal to the cube of the first term, plus three times the square of the first term by the second term, plus three times the first term by the square of the second term, plus the cube of the second term.solution:(x)3+3(x)2(5y)+3(x)(5y)2+(5y)3

answer:x3+3x5y+3x25y+125y

DANIEL PAUL PEREZCUBE OF A BINOMIAL

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∗AVERAGE QUESTION: (5m + 2n)3

solution:(5m)3 + 3.(5m)2. (2n) + 3. (5m). (2n)2 + (2n)3

The sum of a cubed of two binomial is equal to the cube of the first term, plus three times the square of the first term by the second term, plus three times the first term by the square of the second term, plus the cube of the second term.

answer:125 m3 + 150 m2 n + 60 m n2 + 8 n3


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∗CHALLENGING QUESTION:(2p^3-4r)^3

The sum of a cubed of two binomial is equal to the cube of the first term, plus three times the square of the first term by the second term, plus three times the first term by the square of the second term, plus the cube of the second term.solution:(2p^3)^3(2p^3)^2(-4r)+3(2p^3)(-4r)^2+(-4r)^3

answer:8p^9-48p^6^r+96p^3^r^2-64r^3


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NAME OF STUDENT 4


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Name:SQUARE OF A BINOMIAL● EASY QUESTION:

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Name:SQUARE OF A BINOMIAL● AVERAGE QUESTION:

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Name:SQUARE OF A BINOMIAL● CHALLENGING QUESTION:

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Name:Product of Sum and Difference of Two Terms● EASY QUESTION:

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Name:Product of Sum and Difference of Two Terms● AVERAGE QUESTION:

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Name:Product of Sum and Difference of Two Terms● CHALLENGING QUESTION:

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Name:SQUARE OF A TRINOMIAL● EASY QUESTION:

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Name:SQUARE OF A TRINOMIAL● AVERAGE QUESTION:

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Name:SQUARE OF A TRINOMIAL● CHALLENGING QUESTION:

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Name:PRODUCT OF A BINOMIAL AND A TRINOMIAL● EASY QUESTION:

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Name:PRODUCT OF A BINOMIAL AND A TRINOMIAL● AVERAGE QUESTION:

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Name:PRODUCT OF A BINOMIAL AND A TRINOMIAL● CHALLENGING QUESTION:

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Name:CUBE OF A BINOMIAL● EASY QUESTION:

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Name:CUBE OF A BINOMIAL● AVERAGE QUESTION:

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Name:CUBE OF A BINOMIAL● CHALLENGING QUESTION:

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RECLECTIONGroup Name ____


1 2

3 4

JUSTIN BACON


1 23 4

RAFAEL BIAG


1 23 4

DANIEL PAUL PEREZ

This peta was so easy but if i getting to finish its getting harder but i know my work is not the best but i do my best for it to finish this icl peta so if i get a lower score its ok because i just do my best for it and this peta it was fun because this peta we are not using paper work material so we can help mother earth improve so we use the power of electronics.


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Name of Member 4


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Education

Second Quarter Group F Math Peta - Special Products (Sq. of Bi, Sq. of Tri, SDTT, Bi-Tri, Cu. of Bi)