The factors of the expression 1 + 1000 y 3 .

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 80E

1y13y

To determine

To calculate: The factors of the expression 1+1000y3 .

Expert Solution

The factors of the expression 1+1000y3 are (1+10y) and (110y+100y2) .

Explanation of Solution

Given information:

The expression 1+1000y3 .

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 1+1000y3 .

Rewrite it as,

1+1000y3=(1)3+(10y)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=1 and Y=10y .

1+1000y3=(1)3+(10y)3=(1+10y)((1)2(1)(10y)+(10y)2)=(1+10y)(110y+100y2)

Thus, the factors of expression 1+1000y3 are (1+10y) and (110y+100y2) .

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