body{margin:0;} noscript{z-index: 10000; position: fixed; display: block; height: 100%; width: 100%; background: #fff;} noscript .fa{font-size: 40px; display:block; color: #daa520;} noscript div{margin-top: 6%; padding-left: 20px; padding-right: 20px; text-align: center;} ! You must have JavaScript enabled to use this site.

McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

8. Differences of Squares

Continue to next subchapter

Exercise 4 Page 60

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

2p(p+9)(p-9)

Practice makes perfect

To factor the given expression, we will first identify and factor out the greatest common factor. Then, we will use the formula for the difference of two squares.

Factor Out the GCF

The greatest common factor (GCF) of an expression is a common factor of the terms in the expression. It is the common factor with the greatest coefficient and the greatest exponent. The GCF of the given expression is 2p.

2p^3-162p

SplitIntoFactors

Split into factors

2p* p^2- 2p* 81

Factor out 2p

2p(p^2-81)

Difference of Squares

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

p^2-81

Write as a power

p^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. 2p ( p^2- 9^2 ) ⇔ 2p( p+ 9)( p- 9)

Checking Our Answer

Check your answer ✓

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

2p (p + 9) (p - 9)

Distribute 2p

(2p^2 + 18p) (p - 9)

Distribute 2p^2 + 18p

p (2p^2 + 18p) - 9 (2 p^2 + 18 p)

Distribute p

2 p^3 + 18 p^2 - 9(2 p^2 + 18 p)

Distribute -9

2 p^3 + 18 p^2 - 18 p^2 - 162 p

Subtract term

2 p^3 - 162p

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.60-63