   Chapter 0.3, Problem 25E

Chapter
Section
Textbook Problem

In Exercises 23–30, factor each expression and simplify as much as possible. ( x 2 + 1 ) 5 ( x + 3 ) 4 + ( x 2 + 1 ) 6 ( x + 3 ) 3

To determine

To calculate: The factors of the expression (x2+1)5(x+3)4+(x2+1)6(x+3)3 and write it in the simplest form.

Explanation

Given information:

The expression, (x2+1)5(x+3)4+(x2+1)6(x+3)3.

Formula used:

Steps to calculate the factors,

Step1: Factor out the common factor.

Step2: Simplify the remaining terms.

Calculation:

Consider the expression,

(x2+1)5(x+3)4+(x2+1)6(x+3)3

Rewrite the above expression as below,

(x2+1)5(x+3)3(x+3)+(x2+1)5(x2+1)(x+3)3

As both the term contains the term (x2+1)5(x+3)3. Thus, the common factor is (x2+1)5(x+3)3

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