BuyFind

Precalculus: Mathematics for Calcu...

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

Precalculus: Mathematics for Calcu...

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

Solutions

Chapter 1, Problem 53RE
To determine

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

Expert Solution

Answer to Problem 53RE

The answer is 2x36x2+4x .

Explanation of Solution

Given information:

  x2(x2)+x(x2)2

Formula used:

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

  =ac+ad+bc+bd

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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