# The simplified value of the expression ( 2 u + v ) 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 31E
To determine

## To calculate: The simplified value of the expression (2u+v)2 .

Expert Solution

The value of the expression (2u+v)2 is 4u2+4uv+v2 .

### Explanation of Solution

Given information:

The expression (2u+v)2 .

Formula used:

The special product formula of perfect square to multiply the algebraic expressions is mathematically expressed as,

(A+B)2=A2+2AB+B2

Calculation:

Consider the given expression (2u+v)2 .

Recall the special product formula of perfect square to multiply the algebraic expressions is mathematically expressed as,

(A+B)2=A2+2AB+B2

Apply it,

(2u+v)2=(2u)2+2(2u)(v)+(v)2=4u2+4uv+v2

Thus, the value of the expression (2u+v)2 is 4u2+4uv+v2 .

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