Solve Factoringbinomialsasdifferenceofsquares 2x-3=8x^3-12x^2 ...

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation : 2*x-3-(8*x^3-12*x^2)=0

Step by step solution :

Step 1 :

Equation at the end of step 1 :

Step 2 :

Equation at the end of step 2 :

Step 3 :

Checking for a perfect cube :

3.1 -8x3+12x2+2x-3 is not a perfect cube

Trying to factor by pulling out :

3.2 Factoring: -8x3+12x2+2x-3 Thoughtfully split the expression at hand into groups, each group having two terms :Group 1: 2x-3 Group 2: -8x3+12x2 Pull out from each group separately :Group 1: (2x-3) • (1)Group 2: (2x-3) • (-4x2) -------------------Add up the two groups : (2x-3) • (1-4x2) Which is the desired factorization

Trying to factor as a Difference of Squares :

3.3 Factoring: 1-4x2 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 - B2Note : 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 : 4 is the square of 2Check : x2 is the square of x1 Factorization is : (1 + 2x) • (1 - 2x)

Equation at the end of step 3 :

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 separatelyIn other words, we are going to solve as many equations as there are terms in the productAny solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation :

4.2 Solve : 2x+1 = 0Subtract 1 from both sides of the equation : 2x = -1 Divide both sides of the equation by 2: x = -1/2 = -0.500

Solving a Single Variable Equation :

4.3 Solve : -2x+1 = 0Subtract 1 from both sides of the equation : -2x = -1 Multiply both sides of the equation by (-1) : 2x = 1 Divide both sides of the equation by 2: x = 1/2 = 0.500

Solving a Single Variable Equation :

4.4 Solve : 2x-3 = 0Add 3 to both sides of the equation : 2x = 3 Divide both sides of the equation by 2: x = 3/2 = 1.500

Three solutions were found :

1. x = 3/2 = 1.500
2. x = 1/2 = 0.500
3. x = -1/2 = -0.500