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Factoring Trinomials and Special Binomials. In the form ax 2 +bxy+cy 2 and ax 2 – cy 2. Which will ADD to give -18 (1)(72) (2)(36) (3)(24) (4)(18) (6)(12) Yes. NO. GCF?. This sign tells the sign of The larger factor. This sign tells what to do with the factors. - PowerPoint PPT Presentation
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Factoring Trinomials and Special Binomials
In the form ax2+bxy+cy2
and ax2 – cy2
2 29 18 8x xy y
First term in first spot
29x 28y
18xy
2 272x y
Which will ADD to give -18 (1)(72) (2)(36) (3)(24) (4)(18) (6)(12) Yes
Th
is sign
tells w
hat to
do
with
the
factors
Th
is sign
tells th
e sign
of
Th
e larger facto
r
Last term in next spotNow multiply across
Time to factor each column down. Start with third column.
xy
xy
612
y
y
(1)(8) (2)(4)
24
xx
33
Multiply across each row to check your products and up each column also. Then write your answer!!
(3 4 )x y (3 2 )x y
2 214 48x xy y
2x 248y 2 248x y
14xyxy
xy
Which will ADD to give +14
(1)(48) (2)(24) (3)(16) (4)(12) (6)(8) YES
6
8
y
y
68
xx
( 8 )x y ( 6 )x y
2 24 12 9x xy y
24x 29y2 236x y
12xy
Which will ADD to give +12
(1)(36) (2)(18) (3)(12) (4)(9) (6)(6) YES
xy
xy
6
6
y
y
3
3
xx
2
2
(2 3 )x y (2 3 )x y 2(2 3 )x y
Tic-tac-toe can be used with binomials only if the terms are perfect squares and the sign between them is minus!!
They have to be perfect squares so that the middle term will cancel.
These problems are called the difference of two squares.
2 24 9x y2 25x
2 81x This is theFirst term!
This is theLast term!
The middle termDisappeared, orBecame ZERO!!
2x 81 281x
0xx
What factors of -81 willAdd up to be ZERO ?
99
99
xx
( 9)x ( 9)x
2 25x REMEMBERThis is theFirst term!
ANDThis is theLast term!
The middle termDisappeared, orBecame ZERO!!
2x 25 225xxx
What factors of -25 willAdd up to be ZERO ?
055
5
5xx
( 5)x ( 5)x
2 24 9x yThis is theFirst term!
This is theLast term!
The middle termDisappeared, orBecame ZERO!!
The signIs MINUS
So follow theSame steps.
24x 29y 2 236x y
xy
xy0
What factors of -36 willAdd up to be ZERO ?
66
y
y
33
xx
22(2 3 )x y (2 3 )x y
2 29 16x y
29x 216y 2 2144x y
xy
xy0
1212
y
y44
xx
33
(3 4 )x y (3 4 )x y
24 9
25 100x
Check each piece of the problem!!If they are ALL perfect squares, then
follow the same steps!! You just have to factorTop and bottom for each fraction!!
24
25x
9
100 36
2500
0
To see if any number is a Perfect square, find its
Square root!! If you get a Whole number for an answer
then it is a prefect square.6
50
6
50
3
103
10
x
x
2
52
52 3
5 10x
2 3
5 10x
29 1
16 4x
Check each piece of the problem!!If they are ALL perfect squares, then
follow the same steps!! You just have to factorTop and bottom for each fraction!!
29
16x
1
4 29
64x
03
8x
3
8x
1
21
2
x
x
3
43
43 1
4 2x
3 1
4 2x
There is a short-cut for The Difference of Two Squares.
Answer these questions for each problem.* First term a perfect square?* Last term a perfect square?* Minus between them?
• If they all answer yes, then just write your answers!! Watch…29 4x (3 2)(3 2)x x
