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McGraw Hill Integrated II, 2012 View details

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Exercise 65 Page 84

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

(y+9)(y-9)

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Look closely at the expression y^2-81. It can be expressed as the difference of two perfect squares.

y^2-81

WritePow

Write as a power

y^2-9^2

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. ( y^2- 9^2 ) ⇔ ( y+ 9)( y- 9)

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

(y+9) (y-9)

Distr

Distribute (y-9)

y(y-9)+9(y-9)

Distr

Distribute y

y^2-9y+9(y-9)

Distr

Distribute 9

y^2-9y+9y-81

SubTerm

Subtract term

y^2-81

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

1 Adding and Subtracting Polynomials p.81

2 Multiplying a Polynomial by a Monomial p.81

3 Multiplying Polynomials p.81

4 Special Products p.82

5 Using the Distributive Property p.82

6 Solving x^2+bx+c=0 p.83

7 Solving ax^2+bx+c=0 p.83

8 Differences of Squares p.84

9 Perfect Squares p.84

10 Roots and Zeros p.85

Exercise 65 Page 84

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