Question

what is the algebraic expression of 3x²-4​

Answer 1

Step by Step 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 :

                    3*x^2-4-(8)=0  

Step by step solution :

STEP

1

:

Equation at the end of step 1

 (3x2 -  4) -  8  = 0  

STEP

2

:

STEP

3

:

Pulling out like terms

3.1     Pull out like factors :

  3x2 - 12  =   3 • (x2 - 4)  

Trying to factor as a Difference of Squares:

3.2      Factoring:  x2 - 4  

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 : 4 is the square of 2

Check :  x2  is the square of  x1  

Factorization is :       (x + 2)  •  (x - 2)  

Equation at the end of step

3

:

 3 • (x + 2) • (x - 2)  = 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.