# To simplify x 2 ( x − 2 ) + x ( x − 2 ) 2 by using appropriate operations.

### 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, Problem 53RE
To determine

## To simplify x2(x−2)+x(x−2)2 by using appropriate operations.

Expert Solution

### Explanation of Solution

Given information:

x2(x2)+x(x2)2

Formula used:

Distributive property:- (a+b)(c+d)=a(c+d)+b(c+d)

Square of a difference :- (AB)2=A22AB+B2

Calculations:

(x2)2=x22(x)(2)+(2)2

=x24x+4

By using distributive property we get,

x2(x2)=x2(x)x2(2)

=x32x2 (i)

x(x2)2=x(x24x+4)

=x(x2)x(4x)+x(4)

=x34x2+4x  (ii)

Now , adding equation (i) and (ii)

=x32x2+x34x2+4x

=(x3+x3)+(2x24x2)+4x (Combining like terms)

=2x36x2+4x

After simplifying we get 2x36x2+4x .

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