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McGraw Hill Integrated II, 2012

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McGraw Hill Integrated II, 2012 View details

9. Perfect Squares

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Exercise 69 Page 71

The formula to factor the difference of two squares is a^2-b^2=(a+b)(a-b).

(5n+1)(5n-1)

Practice makes perfect

Look closely at the expression 25n^2-1. It can be expressed as the difference of two perfect squares.

25n^2-1

Write as a power

5^2n^2-1^2

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

(5n)^2-1^2

Recall the formula to factor a difference of squares. a^2- b^2 ⇔ ( a+ b)( a- b) We can apply this formula to our expression. ( 5n)^2- 1^2 ⇔ ( 5n+ 1)( 5n- 1)

Checking Our Answer

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We can apply the Distributive Property and compare the result with the given expression.

(5n+1)(5n-1)

Distribute (5n+1)

5n(5n+1)-(5n+1)

Distribute 5n

25n^2+5n-(5n+1)

Distribute -1

25n^2+5n-5n-1

Subtract term

25n^2-1

After applying the Distributive Property and simplifying, the result is the same as the given expression. Therefore, we can be sure our solution is correct!

Subchapter links

Exercises p.68-71