# The factor of the expression ( x − 1 ) 7 2 − ( x − 1 ) 3 2 .

### 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 92E
To determine

## To calculate: The factor of the expression (x−1)72−(x−1)32 .

Expert Solution

The factor of the expression (x1)72(x1)32 is x(x2)(x1)3 .

### Explanation of Solution

Given information:

The expression (x1)72(x1)32 .

Formula used:

To factor an expression, split the terms in the expression into multiplication of simpler expressions, then take the common power out and group the expressions together.

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

(AB)2=A22AB+B2

Calculation:

Consider the given expression (x1)72(x1)32 .

Recall that to factor an expression, split the terms in the expression into multiplication of simpler expressions, then take the common power out and group the expressions together.

The greatest common factor of these terms is (x1)32 .

Apply it,

(x1)72(x1)32=(x1)32[(x1)72(x1)321]=(x1)32[(x1)72321]=(x1)32[(x1)21]

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

(AB)2=A22AB+B2

So, (x1)32[(x1)21] will be further simplified as,

(x1)72(x1)32=(x1)32[(x1)21]=(x1)32[(x)22(x)(1)+121]=(x1)3[x22x]=(x1)3[x(x2)]

It can be rewritten as,

(x1)72(x1)32=x(x2)(x1)3

Thus, the factor of expression (x1)72(x1)32 is x(x2)(x1)3 .

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