   Chapter 0.6, Problem 13E

Chapter
Section
Textbook Problem

Solve the equations in Exercises 1–26. ( x + 1 ) 2 ( 2 x + 3 ) − ( x + 1 ) ( 2 x + 3 ) 2 = 0

To determine

To calculate: The solution of the equation (x+1)2(2x+3)(x+1)(2x+3)2=0.

Explanation

Given information:

The equation, (x+1)2(2x+3)(x+1)(2x+3)2=0.

Formula used:

Zero product property,

If a product of two number is zero, one of the two must be zero.

Calculation:

Consider the expression,

(x+1)2(2x+3)(x+1)(2x+3)2=0

The left side expression is (x+1)2(2x+3)(x+1)(2x+3)2.

As both the term contains the term (x+1)(2x+3). Thus, the common factor is (x+1)(2x+3).

Now, factor out the common factor and simplify as below,

(x+1)2(2x+3)(x+1)(2x+3)2=(x+1)(2x+3)(x+1(2x+3))=(x+1)(2x+3)(x+12x3)=(x+1)(2x+3)(x2)

Therefore, the factors of the expression (x+1)2(2x+3)(x+1)(2x+3)2 are (x+1)(2x+3)(x2)

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