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Intermediate Algebra

10th Edition
Jerome E. Kaufmann + 1 other
ISBN: 9781285195728

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Chapter
Section
BuyFindarrow_forward

Intermediate Algebra

10th Edition
Jerome E. Kaufmann + 1 other
ISBN: 9781285195728
Textbook Problem

For Problems 51 68 , use the sum-of-two-cubes or the difference-of-two-cubes pattern to factor each of the following. (Objective 2)

1 27 a 3 .

To determine

To factor:

The given problem by the use of the sum-of-cubes pattern or the difference-of-cubes pattern.

Explanation

Approach:

i) The Sum of Two Cubes pattern is a3+b3=(a+b)(a2ab+b2).

ii) The Difference of Two Squares pattern is a3b3=(ab)(a2+ab+b2).

iii) Multiplication is commutative, so the order of writing the factors is not important. For example, (ab)(a2+ab+b2) can also be written as (a2+ab+b2)(ab).

The following steps have been followed to find out the factors:

Step-1: Convert the polynomial in the form of 2 cubes with addition or subtraction and compare with the sum of two cubes pattern or the difference of two cubes pattern.

Step-2: Replace the value of a and b in the sum of two cubes pattern or in the difference of two cubes pattern by the binomial values available from the step-2 and simplify.

Calculation:

The given polynomial is 127a3.

It can be written as,

127a3=1333a3=13(3a)3

Because, 13=111=1 and 33=333=27

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