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McGraw Hill Integrated II, 2012
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McGraw Hill Integrated II, 2012 View details
Study Guide and Review
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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)

Practice makes perfect

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)

Checking Our Answer

 Check your answer ✓
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 expand_more
arrow_right 1 Adding and Subtracting Polynomials p.81
11
Adding and Subtracting Polynomials 12 (Page 81)
Adding and Subtracting Polynomials 13 (Page 81)
Adding and Subtracting Polynomials 14 (Page 81)
Adding and Subtracting Polynomials 15 (Page 81)
Adding and Subtracting Polynomials 16 (Page 81)
Adding and Subtracting Polynomials 17 (Page 81)
Adding and Subtracting Polynomials 18 (Page 81)
arrow_right 2 Multiplying a Polynomial by a Monomial p.81
Multiplying a Polynomial by a Monomial 19 (Page 81)
Multiplying a Polynomial by a Monomial 20 (Page 81)
Multiplying a Polynomial by a Monomial 21 (Page 81)
Multiplying a Polynomial by a Monomial 22 (Page 81)
arrow_right 3 Multiplying Polynomials p.81
Multiplying Polynomials 23 (Page 81)
Multiplying Polynomials 24 (Page 81)
Multiplying Polynomials 25 (Page 81)
Multiplying Polynomials 26 (Page 81)
Multiplying Polynomials 27 (Page 81)
arrow_right 4 Special Products p.82
Special Products 28 (Page 82)
Special Products 29 (Page 82)
Special Products 30 (Page 82)
Special Products 31 (Page 82)
Special Products 32 (Page 82)
Special Products 33 (Page 82)
Special Products 34 (Page 82)
arrow_right 5 Using the Distributive Property p.82
Using the Distributive Property 35 (Page 82)
Using the Distributive Property 36 (Page 82)
Using the Distributive Property 37 (Page 82)
Using the Distributive Property 38 (Page 82)
Using the Distributive Property 39 (Page 82)
Using the Distributive Property 40 (Page 82)
Using the Distributive Property 41 (Page 82)
Using the Distributive Property 42 (Page 82)
Using the Distributive Property 43 (Page 82)
Using the Distributive Property 44 (Page 82)
Using the Distributive Property 45 (Page 82)
arrow_right 6 Solving x^2+bx+c=0 p.83
Solving x^2+bx+c=0 46 (Page 83)
Solving x^2+bx+c=0 47 (Page 83)
Solving x^2+bx+c=0 48 (Page 83)
Solving x^2+bx+c=0 49 (Page 83)
Solving x^2+bx+c=0 50 (Page 83)
Solving x^2+bx+c=0 51 (Page 83)
Solving x^2+bx+c=0 52 (Page 83)
Solving x^2+bx+c=0 53 (Page 83)
Solving x^2+bx+c=0 54 (Page 83)
Solving x^2+bx+c=0 55 (Page 83)
arrow_right 7 Solving ax^2+bx+c=0 p.83
Solving ax^2+bx+c=0 56 (Page 83)
Solving ax^2+bx+c=0 57 (Page 83)
Solving ax^2+bx+c=0 58 (Page 83)
Solving ax^2+bx+c=0 59 (Page 83)
Solving ax^2+bx+c=0 60 (Page 83)
Solving ax^2+bx+c=0 61 (Page 83)
Solving ax^2+bx+c=0 62 (Page 83)
Solving ax^2+bx+c=0 63 (Page 83)
Solving ax^2+bx+c=0 64 (Page 83)
arrow_right 8 Differences of Squares p.84
Differences of Squares 65 (Page 84)
Differences of Squares 66 (Page 84)
Differences of Squares 67 (Page 84)
Differences of Squares 68 (Page 84)
Differences of Squares 69 (Page 84)
Differences of Squares 70 (Page 84)
Differences of Squares 71 (Page 84)
Differences of Squares 72 (Page 84)
Differences of Squares 73 (Page 84)
arrow_right 9 Perfect Squares p.84
Perfect Squares 74 (Page 84)
Perfect Squares 75 (Page 84)
Perfect Squares 76 (Page 84)
Perfect Squares 77 (Page 84)
Perfect Squares 78 (Page 84)
Perfect Squares 79 (Page 84)
Perfect Squares 80 (Page 84)
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Perfect Squares 82 (Page 84)
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arrow_right 10 Roots and Zeros p.85
Roots and Zeros 85 (Page 85)
Roots and Zeros 86 (Page 85)
Roots and Zeros 87 (Page 85)
Roots and Zeros 88 (Page 85)
Roots and Zeros 89 (Page 85)