Chapter 0, Problem 11PO

To determine

To calculate: The factored expression of the given polynomial.

Answer to Problem 11PO

The factored expression is $(2x+y)(2x+y)$ .

Explanation of Solution

Given information: The given polynomial is $4x^2+4xy+y^2$ .

Calculation:

The given polynomial is $4x^2+4xy+y^2$ .

The formula for ${(a+b)}^2$ is $a^2+2ab+b^2$ .

By factoring the polynomial,

  $\begin{array}{l}4x^2+4xy+y^2\\ $ ={(2x)}^2+2\cdot 2x\cdot y+{(y)}^2$$ ={(2x+y)}^2$=(2x+y)(2x+y)\end{array}$

  $\therefore$ The factored expression is $(2x+y)(2x+y)$ .