factor using gcf difference of squares · difference of squares is a special type of factoring only...
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Factor usingDifference of Squares
Factor using GCF
Factoring Binomials
Factoring Binomials using Difference of Squares
Difference Answer to a subtraction problem
Squares Perfect SquareProducts of numbers that are multiplied by themselves2 2 = 22 = 4
6 6 = 62 = 36
perfect square
perfect square
Difference of Squares Illustrated by Algebra TilesHow can we represent x2 9 with algebra tiles?
Only way to make a rectangle (square) is if there is 3 positive bars and 3 negative bars. The zero sum total "cancels" the bars out in the equation.
Must be able to recognizea perfect square in order to
factor using difference of squares.
There will be a quiz on ___________ over all of the perfect squares from 1 to 400.
H
Remember that perfect squares are the products of numbers that are multiplied by themselves!
Perfect Squares between 140012 = 1 62 = 36 112 = 121 162 = 25622 = 4 72 = 49 122 = 144 172 = 28932 = 9 82 = 64 132 = 169 182 = 32442 = 16 92 = 81 142 = 196 192 = 36152 = 25 102 = 100 152 = 225 202 = 400
Difference of Squares is a special type of factoring
ONLY for binomials.
Both must be true to factor using Difference of Squares.
1. Operation between terms must be subtraction.
2. All numbers and variables must be perfect squares.
Perfect Squares with Variables
4 = 2 2 16 = 4 4so that means...
x2 = x x x4 = x2 x2
x2 is a perfect squarex4 is a perfect square
x# is a perfect square if the exponent is even
Factor.4x2 9y2
An actual TN Ready question from a previous test.
Select all of the expressions equivalent to 162x2 72.
(a) 2(9x 6)2
(b) 2(81x2 36)
(c) 2(9x 6)(9x + 6)
(d) 18(3x2 2)2
(e) 18(3x 2)(3x + 2)
Factoring Possibilities w/ BinomialsWhen factoring a binomial, there are only 3 possibilities:
1. GCF only [Binomial is being added/not perfect square.]
2. No GCF, factor using Difference of Squares
3. Factor using GCF and Difference of Squares
Factor the following:
1) 25x2 49 2) 12x4 27x2
3) 14x2y3 + 18y2 4) 169x2y2 196
1) 25x2 49 2) 12x4 27x2Binomial BinomialNo GCF GCF > 3x2(4x2 9)DOS > (5x 7)(5x + 7) DOS > 3x2(2x 3)(2x + 3)
(5x 7)(5x + 7) 3x2(2x 3)(2x + 3)
3) 14x2y3 + 18y2 4) 169x2y2 196Binomial BinomialGCF > 2y2(7x2y + 9) No GCF No DOS (No Difference) DOS > (13xy 14)(13xy + 14)
2y2(7x2y + 9) (13xy 14)(13xy + 14)
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