# The factor of the expression 4 x 2 + 4 x y + y 2 .

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

Chapter 1.3, Problem 107E
To determine

## To calculate: The factor of the expression 4x2+4xy+y2 .

Expert Solution

The factor of the expression 4x2+4xy+y2 is (2x+y)2 .

### Explanation of Solution

Given information:

The expression 4x2+4xy+y2 .

Formula used:

The special factoring formula of perfect square which is expressed as,

X2+2XY+Y2=(X+Y)2

Calculation:

Consider the given expression 4x2+4xy+y2 .

Rewrite it as,

4x2+4xy+y2=(2x)2+2(2x)(y)+(y)2

Recall the special factoring formula of perfect square which is expressed as,

X2+2XY+Y2=(X+Y)2

Here, the values of X and Y are X=2x and Y=y .

4x2+4xy+y2=(2x)2+2(2x)(y)+(y)2=(2x+y)2

Thus, the factor of expression 4x2+4xy+y2 is (2x+y)2 .

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