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Chapter 7: Q 270 (page 868)

In the following exercises, factor.

27u3+1000

Short Answer

Expert verified

The factorization of the expression is(3u+10)(9u2-30u+100)

Step by step solution

01

Step 1. Given information

Given expression is27u3+1000

02

Step 2. Write the terms as a cube.

a3+b3=(3u)3+(10)3

03

Step 3.  Write the sum in the cubes pattern and simplify.

(a+b)(a2-ab+b2)=(3u+10)(3u)2-3u脳10+(10)2=(3u+10)(9u2-30u+100)

04

Step 4. Check

(3u+10)(9u2-30u+100)=27u3+90u2-90u2-300u+300u+1000=27u3+1000

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