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Chapter 6: Q. 203 (page 603)

In the following exercises, factor completely using the sums and differences of cubes pattern, if possible.
216a3+125b3

Short Answer

Expert verified

The factored form of the given expression is (6a+5b)(36a2-30ab+25b2).

Step by step solution

01

Step 1. Given information.

The given expression is:
216a3+125b3

02

Step 2. Determine the factored form.

The given expression can be written as:
216a3+125b3=(6a)3+(5b)3=(6a+5b)((6a)2-(6a)(5b)+(5b)2)鈭�a3+b3=(a+b)(a2-ab+b2)=(6a+5b)(36a2-30ab+25b2)

03

Step 3. Conclusion.

The factored form of the given expression is (6a+5b)(36a2-30ab+25b2).

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