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Chapter 6: Q. 402 (page 636)

In the following exercises, factor completely using the sums and differences of cubes pattern, if possible.

b3鈭�216

Short Answer

Expert verified

The Factored form of given polynomial is,

(b-6)b2+6b+36

Step by step solution

01

Step 1. Given Information

We are given a polynomial,

b3鈭�216

The formula used for factoring using sum and difference of cube is,

(a3-b3)=(a-b)(a2+ab+b2)(a3+b3)=(a+b)(a2-ab+b2)

02

Step 2. Factorizing the polynomial 

The given polynomial can be also written as,

b3鈭�216=(b)3-(6)3

Using (a3-b3)=(a-b)(a2+ab+b2), we get

b3鈭�216=(b-6)b2+b脳6+62b3鈭�216=(b-6)b2+6b+36

03

Step 3. Checking the factorization by multiplying

Multiplying the factors, we get

(b-6)b2+6b+36=b3鈭�216b3+6b2+36b-6b2-36b-216=b3鈭�216b3鈭�216=b3鈭�216LHS=RHS

Hence the factorization is correct.

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