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McGraw Hill Integrated II, 2012 View details

1. Solving Quadratic Equations by Factoring

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Exercise 81 Page 176

Begin by factoring the GFC(greatest common factor) out and writing the expression as the difference of cubes.

5x^2(2x-3y)(4x^2+6xy+9y^2)

Practice makes perfect

When factoring a binomial that is a difference of cubes, there is a general rule we can use. a^3-b^3=(a-b)(a^2+ab+b^2)Let's begin by factoring the GFC(greatest common factor) out and writing the expression as the difference of cubes.

40x^5-135x^2y^3

FactorOut

Factor out 5x^2

5x^2(8x^3-27y^3)

WritePow

Write as a power

5x^2(2^3x^3-3^3y^3)

ProdPow

a^m* b^m=(a * b)^m

5x^2((2x)^3-(3y)^3)

Now, we can apply the rule. 5x^2((2x)^3-(3y)^3) ⇓ 5x^2(2x-3y)(4x^2+6xy+9y^2)