Exercise 28 Page 69

Let's start by rewriting the given expression so terms with common factors are near one another. x^3 +2x^2y -4x -8y ⇕ x^3 -4x +2x^2y -8yNow we will take the greatest common factor of each group so we can factor by grouping.

x^3 - 4x+2x^2y-8y

FactorOut

Factor out x

x( x^2-4) + 2x^2y - 8y

FactorOut

Factor out 2y

x( x^2-4 ) +2y( x^2-4 )

Notice that (x^2-4) is a factor of both terms, so we can factor it out. Moreover, (x^2-4) is the difference of two squares, so we can rewrite is as (x+2)(x-2).

x( x^2-4 ) +2y( x^2-4 )

FactorOut

Factor out ( x^2-4 )

( x^2-4 ) ( x+2y )

FacDiffSquares

a^2-b^2=(a+b)(a-b)

( x+2 )(x-2) ( x+2y )