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Chapter 7: Q. 429 (page 900)

Factor Sums and Differences of Cubes

In the following exercises, factor.

a3-125

Short Answer

Expert verified

The factors fora3-125=(a-5)(a2+5a+25)

Step by step solution

01

Step 1. Given information

The given differences of cubes a3-125

02

Step 2. Finding the factors for given differences of cubes 

We can find the factors as follows

Use the sum product pattern

a3-125=a3-53[鈭�(a3-b3)=(a-b)(a2+ab+b2)]=a3+5a2+25a-5a2-25a-125

Common factors from the two pairs

a3+5a2+25a-5a2-25a-125=a(a2+5a+25)-5(a2+5a+25)

Rewrite in factored form

a(a2+5a+25)-5(a2+5a+25)=(a-5)(a2+5a+25)

Therefore,the factors fora3-125=(a-5)(a2+5a+25)

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Most popular questions from this chapter

Factor by grouping

x2+7x鈭�3x鈭�21

A boat鈥檚 sail is a right triangle. The length of one side of the sail is 7 feet more than the other side. The hypotenuse is 13. Find the lengths of the two sides of the sail.

Factor:-16z-64.

In the following exercises, solve:

y2=y+132.

Factor Differences of Squares

In the following exercises, factor.

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