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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

9. Perfect Squares

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Exercise 29 Page 69

Rewrite the given expression so that it is easier to make groups.

2a(b+1)(b-1)(a-b)

Practice makes perfect

To factor by grouping, we will take the greatest common factor of the first pair of terms and the greatest common factor of the second pair of terms.

2a^2b^2 - 2a^2-2ab^3+2ab

Factor out 2a^2

2a^2( b^2-1 ) - 2ab^3 + 2ab

Factor out -2ab

2a^2( b^2-1 ) -2ab( b^2-1 )

Notice that (b^2-1) and 2a are factors of both terms, so we can factor them out.

2a^2( b^2-1 ) -2ab( b^2-1 )

Factor out ( b^2-1 )

( b^2-1 ) ( 2a^2-2ab )

Factor out 2a

2a(b^2-1)(a-b)

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

2a(b+1)(b-1)(a-b)

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Exercises p.68-71