Question

${x}^{3} \div x$

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Answer 1

Answer:

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Step-by-step explanation:

Changes made to your input should not affect the solution:

(1): "x3"   was replaced by   "x^3".  

Step by step solution :

STEP

1

:

STEP

2

:

Pulling out like terms

2.1     Pull out like factors :

  x3 - x  =   x • (x2 - 1)  

Trying to factor as a Difference of Squares:

2.2      Factoring:  x2 - 1  

Theory : A difference of two perfect squares,  A2 - B2  can be factored into  (A+B) • (A-B)

Proof :  (A+B) • (A-B) =

        A2 - AB + BA - B2 =

        A2 - AB + AB - B2 =

        A2 - B2

Note :  AB = BA is the commutative property of multiplication.

Note :  - AB + AB equals zero and is therefore eliminated from the expression.

Check : 1 is the square of 1

Check :  x2  is the square of  x1  

Factorization is :       (x + 1)  •  (x - 1)  

Equation at the end of step

2

:

 x • (x + 1) • (x - 1)  = 0  

STEP

3

:

Theory - Roots of a product

3.1    A product of several terms equals zero.  

When a product of two or more terms equals zero, then at least one of the terms must be zero.  

We shall now solve each term = 0 separately  

In other words, we are going to solve as many equations as there are terms in the product  

Any solution of term = 0 solves product = 0 as well.