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Chapter 6: Q. 204 (page 603)

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

27y3+8z3

Short Answer

Expert verified

The factored form of the given expression is (3y+2z)(9y2-6yz+4z2).

Step by step solution

01

Step 1. Given information.

The given expression is:

27y3+8z3

02

Step 2. Determine the factored form.

The given expression can be written as:
27y3+8z3=(3y)3+(2z)3=(3y+2z)((3y)2-(3y)(2z)+(2z)2)鈭�a3+b3=(a+b)(a2-ab+b2)=(3y+2z)(9y2-6yz+4z2)

03

Step 3. Conclusion.

The factored form of the given expression is (3y+2z)(9y2-6yz+4z2).

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