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Chapter 6: Q. 209 (page 604)

In the following exercises, factor completely using the sums and differences of cubes pattern, if possible.
(x+3)3+8x3

Short Answer

Expert verified

The factored form of the given expression is9(x+1)(x2+3).

Step by step solution

01

Step 1. Given information.

The given expression is:
(x+3)3+8x3

02

Step 2. Determine the factored form.

The given expression can be written as:
(x+3)3+8x3=(x+3)3+(2x)3=(x+3+2x)((x+3)2-(x+3)(2x)+(2x)2)鈭�a3+b3=(a+b)(a2-ab+b2)=(3x+3)(x2+6x+9-2x2-6x+4x2)鈭�(a+b)2=a2+2ab+b2=3(x+1)(3x2+9)=9(x+1)(x2+3)

03

Step 3. Conclusion.

The factored form of the given expression is 9(x+1)(x2+3).

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