# The common factor of the expression − 7 x 4 y 2 + 14 x y 3 + 21 x y 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 66E
To determine

## To calculate: The common factor of the expression −7x4y2+14xy3+21xy4 .

Expert Solution

The common factor of the expression 7x4y2+14xy3+21xy4 is 7xy2(x32y3y2) .

### Explanation of Solution

Given information:

The expression 7x4y2+14xy3+21xy4 .

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.

Calculation:

Consider the given expression 7x4y2+14xy3+21xy4 .

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.

Here, the greatest common factor of 7,14 and 21 is 7 .

The greatest common factor of x4,x and x is x .

The greatest common factor of y2,y3 and y4 is y2 .

So, 7x4y2+14xy3+21xy4 can be written in simplified form as,

7x4y2+14xy3+21xy4=7xy2(x32y3y2)

Thus, the common factor of the expression 7x4y2+14xy3+21xy4 is 7xy2(x32y3y2) .

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