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Chapter 7: Q 250. (page 867)

In the following exercises, factor.

n3+512

Short Answer

Expert verified

The factorization ofn3+512is,(n+8)(n2-8n+64).

Step by step solution

01

Step 1. Given information  

Given expression isn3+512.

02

Step 2. Does the binomial fit the sum or difference of cubes pattern?

Is it a sum or difference?

This binomial is a sum.

n3+512

Are the first and last terms perfect cubes?

The first and last terms are perfect cubes.

n3+512

03

Step 3. Write them as cubes

(a)3+(b)3=(n)3+(8)3

04

Step 4. Use either the sum of cubes pattern

(a+b)(a2-ab+b2)=(n+8)(n2-8n+82)

05

Step 5. Simplify inside the parentheses

(n+8)(n2-8n+82)=(n+8)(n2-8n+64)

06

Step 6. Check by multiplying the factors

(n+8)(n2-8n+64)=(n3-8n2+64n+8n2-64n+512)=(n3+512)

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Most popular questions from this chapter

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