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McGraw Hill Integrated II, 2012 View details

Study Guide and Review

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Exercise 78 Page 84

Use the given expression as a difference of the squares.

(x^2+1)(x+1)(x-1)

Practice makes perfect

We want to completely factor the given expression. To do so we will use the difference of the squares.

x^4-1

Rewrite

Rewrite x^4 as (x^2)^2

(x^2)^2-1

Rewrite

Rewrite 1 as 1^2

(x^2)^2-1^2

FacDiffSquares

a^2-b^2=(a+b)(a-b)

(x^2+1)(x^2-1)

Rewrite

Rewrite 1 as 1^2

(x^2+1)(x^2-1^2)

FacDiffSquares

a^2-b^2=(a+b)(a-b)

(x^2+1)(x+1)(x-1)

Checking Our Answer

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We can expand our answer and compare it with the given expression.

(x^2+1)(x+1)(x-1)

ExpandDiffSquares

(a+b)(a-b)=a^2-b^2

(x^2+1)(x^2-1)

ExpandDiffSquares

(a+b)(a-b)=a^2-b^2

(x^2)^2-1^2

BaseOne

1^a=1

(x^2)^2-1

PowPow

(a^m)^n=a^(m* n)

x^4-1

We can see above that after expanding 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 78 Page 84

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