# The factor of the expression y 4 ( y + 2 ) 3 + y 5 ( y + 2 ) 4 .

### 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 122E
To determine

## To calculate: The factor of the expression y4(y+2)3+y5(y+2)4 .

Expert Solution

The factor of the expression y4(y+2)3+y5(y+2)4 is y4(y+2)3(y+1)2 .

### Explanation of Solution

Given information:

The expression y4(y+2)3+y5(y+2)4 .

Formula used:

To factor out the common factor from a polynomial, find out the greatest common factor and express the polynomial as a product of the simpler ones.

The special factoring formula for perfect square, which is mathematically expressed as,

X2+2XY+Y2=(X+Y)2

Calculation:

Consider the given expression y4(y+2)3+y5(y+2)4 .

Recall that to factor out the common factor from a polynomial, find out the greatest common factor and express the polynomial as a product of the simpler ones.

The common factor of these terms is y4(y+2)3 .

Simplify y4(y+2)3+y5(y+2)4 further as,

y4(y+2)3+y5(y+2)4=y4(y+2)3[1+y(y+2)]=y4(y+2)3(1+y2+2y)=y4(y+2)3(y2+2y+1)

Recall the special factoring formula for perfect square, which is mathematically expressed as,

X2+2XY+Y2=(X+Y)2

Apply it to factorize (y2+2y+1) , where X=y and Y=1

y4(y+2)3+y5(y+2)4=y4(y+2)3(y2+2y+1)=y4(y+2)3(y+1)2

Thus, the factor of expression y4(y+2)3+y5(y+2)4 is y4(y+2)3(y+1)2 .

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