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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

8. Differences of Squares

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Exercise 57 Page 62

Recall how to factor difference of squares.

Lorenzo is correct.
Elizabeth's solution has the incorrect exponents on the x-terms.

Practice makes perfect

We need to recall how to factor difference of squares. a^2- b^2=( a- b)( a+ b)To find the factored form of the given expression, let's write it in a^2-b^2 form. 16x^4-25y^2 =( 4x^2)^2- 5y^2 We can now apply the rule. 16x^4-25y^2 & =( 4x^2)^2- 5y^2 & =( 4x^2- 5y)( 4x^2+ 5y) As we can see, Lorenzo's solution is correct, while Elizabeth's solution is incorrect. Elizabeth's factors give us 16x^2-25y^2.

Showing Our Work

Multiplying Factors in Elizabeth's Answer

Let's check Elizabeth's answer.

(4x-5y)(4x+5y)

Multiply parentheses

16x^2+20xy-20xy-25y^2

Subtract term

16x^2-25y^2

We see that the product is equal to 16x^2-25y^2, not 16x^4-25y^2.

Subchapter links

Exercises p.60-63