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McGraw Hill Integrated II, 2012 View details

9. Perfect Squares

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Exercise 20 Page 69

Rewrite the given expression as the difference of the squares.

(4a+11b)(4a-11b)

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We want to completely factor the given expression. There is no common factor between all of the terms. However, notice that this is a difference of squares. Let's rewrite our expression as a binomial multiplied by it's conjugate. 16a^2-121b^2 ⇔ (4a+11b)(4a-11b)

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We can expand our answer and compare it with the given expression.

(4a +11b) (4a - 11b)

Distr

Distribute 4a+11b

4a (4a +11b) - 11b(4a +11b)

Distr

Distribute 4a

16 a^2 + 44ab - 11b(4a +11b)

Distr

Distribute - 11b

16a^2+44ab-44ab-121b^2

SubTerm

Subtract term

16a^2-121b^2

We can see above that after expanding and simplifying, the result is the same as the given expression. Therefore, we can be sure our solution is correct!

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Exercises p.68-71

Exercise 20 Page 69

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