Question

What is the answer / product of 8x2

Answer 1

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "x2"   was replaced by   "x^2".  

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    8*x^2-(8)=0  

Step by step solution :

STEP

1

:

Equation at the end of step 1

 23x2 -  8  = 0  

STEP

2

:

STEP

3

:

Pulling out like terms

3.1     Pull out like factors :

  8x2 - 8  =   8 • (x2 - 1)  

Trying to factor as a Difference of Squares:

3.2      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

3

:

 8 • (x + 1) • (x - 1)  = 0  

STEP

4

:

Theory - Roots of a product

4.1    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.

Equations which are never true:

4.2      Solve :    8   =  0

This equation has no solution.

A a non-zero constant never equals zero.

Solving a Single Variable Equation:

4.3      Solve  :    x+1 = 0  

Subtract  1  from both sides of the equation :  

                     x = -1

Solving a Single Variable Equation:

4.4      Solve  :    x-1 = 0  

Add  1  to both sides of the equation :  

                     x = 1

Two solutions were found :

x = 1

x = -1