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Chapter 6: Q. 212 (page 604)

In the following exercises, factor completely using the sums and differences of cubes pattern, if possible.
(y-5)3+125y3

Short Answer

Expert verified

The factored form of the given expression is (6y-5)(21y2+15y+25).

Step by step solution

01

Step 1. Given information.

The given expression is:
(y-5)3+125y3

02

Step 2. Determine the factored form.

The given expression can be written as:
(y-5)3+125y3=(y-5)3+(5y)3=(y-5+5y)((y-5)2-(y-5)(5y)+(5y)2)鈭�a3+b3=(a+b)(a2-ab+b2)=(6y-5)(y2-10y+25-5y2+25y+25y2)鈭�(a-b)2=a2-2ab+b2=(6y-5)(21y2+15y+25)

03

Step 3. Conclusion.

The factored form of the given expression is (6y-5)(21y2+15y+25).

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