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 1.3, Problem 114E
To determine

To calculate: The factor of the expression x6+64 .

Expert Solution

Answer to Problem 114E

The factor of the expression x6+64 is (x2+4)(x44x2+16) .

Explanation of Solution

Given information:

The expression x6+64 .

Formula used:

The special factoring formula of sum of cubes which is expressed as,

  X3+Y3=(X+Y)(X2XY+Y2)

Calculation:

Consider the given expression x6+64 .

Rewrite it as,

  x6+64=(x2)3+(4)3

Recall the special factoring formula of sum of cubes which is expressed as,

  X3+Y3=(X+Y)(X2XY+Y2)

Here, the values of X and Y are X=x2 and Y=4 .

  x6+64=(x2)3+(4)3=(x2+4)((x2)2(x2)(4)+(4)2)=(x2+4)(x44x2+16)

Thus, the factor of expression x6+64 is (x2+4)(x44x2+16) .

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