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Chapter 7: Q. 294 (page 878)

In the following exercises, factor completely.

64x2+16xy+y2

Short Answer

Expert verified

The factored form of the polynomial is64x2+16xy+y2=(8x+y)2.

Step by step solution

01

Step 1. Given Information.  

The given Polynomial is64x2+16xy+y2.

02

Step 2. Factoring by the formula for the square of the sum of two terms.  

Terms of a polynomial do not have any common factor.

The polynomial is trinomial where the first and last terms are a perfect square.

Trinomial is in the pattern ofa2+2ab+b2.

Factorize it by using the formula for the square of the sum of two terms.

64x2+16xy+y2=(8x)2+16xy+y2=(8x)2+2路8x路y+y2=(8x+y)2

Now polynomial cannot be factored further.

So factored form is64x2+16xy+y2=(8x+y)2.

03

Step 3. Verification.  

Check whether the expanded form of the factored polynomial is equal to the original polynomial or not.

64x2+16xy+y2=?(8x+y)264x2+16xy+y2=?(8x+y)(8x+y)64x2+16xy+y2=?(8x)2+8xy+8xy+y264x2+16xy+y2=64x2+16xy+y2

The left-hand side is equal to the right-hand side so factored form is correct.

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