   Chapter 0.3, Problem 26E

Chapter
Section
Textbook Problem

In Exercises 23–30, factor each expression and simplify as much as possible. 10 x ( x 2 + 1 ) 4 ( x 3 + 1 ) 5 + 15 x 2 ( x 2 + 1 ) 5 ( x 3 + 1 ) 4

To determine

To calculate: The factors of the expression 10x(x2+1)4(x3+1)5+15x2(x2+1)5(x3+1)4 and write it in the simplest form.

Explanation

Given information:

The expression, 10x(x2+1)4(x3+1)5+15x2(x2+1)5(x3+1)4.

Formula used:

Steps to calculate the factors,

Step1: Factor out the common factor.

Step2: Simplify the remaining terms.

The distributive law,

(a±b)c=ac±bc

Where, a, b and c are any real numbers.

Calculation:

Consider the expression,

10x(x2+1)4(x3+1)5+15x2(x2+1)5(x3+1)4

Rewrite the above expression as below,

2×5x(x2+1)4(x3+1)4(x3+1)+3x×5x(x2+1)4(x2+1)(x3+1)4

As both the term contains the term 5x(x2+1)4(x3+1)4. Thus, the common factor is 5x(x2+1)4(x3+1)4

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