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F. Multiplying Two Binomials. O. I. L. To EXPAND two binomials we use a version of the distributive law called FOIL. Step 1 : Multiply the F IRST terms in the brackets. F. Step 2 : Multiply the O UTSIDE terms. O. Step 3 : Multiply the I NSIDE terms. I. - PowerPoint PPT Presentation
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Step 1: Multiply the FIRST terms in the brackets.
)4)(2( xx
2x
Step 2: Multiply the OUTSIDE terms.
)4)(2( xx
xx 42
Step 3: Multiply the INSIDE terms.
)4)(2( xx
xxx 242
Step 4: Multiply the LAST terms.
)4)(2( xx
8242 xxx
Step 5: Collect like terms.
8242 xxx
862 xx
)4)(23( xx
)4)(23( xx
23x x12 x2 8
8143 2 xx
( 3)( 6)x x
(6 7)(2 2)x x
x2 + 10 x + 16 = (x + 2)(x + 8)
x2 + 9x + 20= (x + 5)(x + 4)
x2 + 11x + 24
= (x + 8)(x + 3)
x2 + 5x + 4= (x + 4)(x + 1)
= x2 + 8x + 2x + 16= x2 + 10x + 16
Factoring Simple TrinomialsFactoring Simple Trinomials
Check by FOILing
What relationship is there between
product form and factored form?
Many trinomials can be written as the product of 2 binomials.
Recall: (x + 4)(x + 3) = x2 + 3x + 4x + 12
= x2 + 7x + 12
The middle term of a simple trinomial is the SUM of the last two terms of the binomials.
The last term of a simple trinomial is the PRODUCT of the last two terms of the binomials.
Factoring Simple TrinomialsFactoring Simple Trinomials
Therefore this type of factoring is referred to as SUM-PRODUCT!
1,12 13
2,6 8
3,4 7
x12 +7
(x + 3)(x + 4)
To factor trinomials, you ask yourself…
x2 + 7x + 12
x2 – 8x +12– 8x 12
131, 12-13-1, -12
82, 6-8-2, -6
( x – 2)( x – 6)
Factor:Factor:
m2 – 5m -14 -5x (-14)
13-1, 14-131, -145
-5-2, 72, -7
(m + 2) (m – 7)
Factor:Factor:
x2 - 11x + 24
x2 + 13x + 36
x2 - 14x + 33
Factor:Factor:
x2 + 12x + 32
x2 - 20x + 75
x2 + 4x – 45
x2 + 17x + 72
x2 - 7x – 8
Factor:Factor:
- 5t – 3t2 + 15 + 4t2 – 3 - 3t
Factor:Factor:
t2 – 8t +12STEP 1: Combine
Like terms
- 8x 12131, 12
-13-1, -12
82, 6-8-2, -6
( x – 2)( x – 6)
Factor:Factor:STEP 1:
Pull out the GCF
7q2 – 14q - 21
7 ( q2 –2q –3)
-2-3
2
-2
-1, 3
-3, 1
7 ( q – 3)( q + 1)
To Summarize:To Summarize:1. Always check to see if you can simplify first!2. Then check to see if you can pull out a common
factor.3. Write 2 sets of brackets with x in the first
position.4. Find 2 numbers whose sum is the middle
coefficient, and whose product is the last term.5. Check by foiling the factors.
ex. 22 14 20x x 22( 7 10)x x + = 7
x = 105, 22( 5)( 2)x x
ex.23 3 60x x + = 1
x = -20-4, 5
3( 4)( 5)x x
common factor?
common factor?
23( 20)x x
How could we factor this using algebra tiles?
x + 2
x + 3
1. Create a rectangle using the exact number of tiles in the given expression.
2. Remember that a trinomial represents area – two binomials multiplied together.
3. What is the width and length of the rectangle?
4. These are the FACTORS of the original rectangle.
Does that make
sense?
(x+3)(x+2)
2 3 2x x 2 4 4x x
1. Create a rectangle using the exact number of tiles in the given expression.
2. Remember that a trinomial represents area – two binomials multiplied together.
3. What is the width and length of the rectangle?
4. These are the FACTORS of the original rectangle.
