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McGraw Hill Integrated II, 2012 View details

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Exercise 67 Page 84

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

(4a+sqrt(21)b)(4a-sqrt(21)b)

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Look closely at the expression 16a^2-21b^2. It can be expressed as the difference of two perfect squares.

16a^2-21b^2

WritePow

Write as a power

4^2a^2-sqrt(21)^2b^2

ProdPowII

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

(4a)^2-(sqrt(21)b)^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. ( ( 4a)^2-( sqrt(21)b)^2 ) ⇕ ( 4a+ sqrt(21)b)( 4a- sqrt(21)b)

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

(4a+sqrt(21)b) (4a-sqrt(21)b)

Distr

Distribute (4a-sqrt(21)b)

4a(4a-sqrt(21)b)+sqrt(21)b(4a-sqrt(21)b)

Distr

Distribute 4a

16a^2-4sqrt(21)ab+sqrt(21)b(4a-sqrt(21)b)

Distr

Distribute sqrt(21)b

16a^2-4sqrt(21)ab+4sqrt(21)ab-21b^2

SubTerm

Subtract term

16a^2-21b^2

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 67 Page 84

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