Solution - Factoring binomials using the difference of squares
Step by Step Solution
Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
-32-(-18*x^2)=0
Step by step solution :
Step 1 :
Equation at the end of step 1 :
-32 - (0 - (2•32x2)) = 0
Step 2 :
Step 3 :
Pulling out like terms :
3.1 Pull out like factors :
18x2 - 32 = 2 • (9x2 - 16)
Trying to factor as a Difference of Squares :
3.2 Factoring: 9x2 - 16
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 : 9 is the square of 3
Check : 16 is the square of 4
Check : x2 is the square of x1
Factorization is : (3x + 4) • (3x - 4)
Equation at the end of step 3 :
2 • (3x + 4) • (3x - 4) = 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 : 2 = 0
This equation has no solution.
A a non-zero constant never equals zero.
Solving a Single Variable Equation :
4.3 Solve : 3x+4 = 0
Subtract 4 from both sides of the equation :
3x = -4
Divide both sides of the equation by 3:
x = -4/3 = -1.333
Solving a Single Variable Equation :
4.4 Solve : 3x-4 = 0
Add 4 to both sides of the equation :
3x = 4
Divide both sides of the equation by 3:
x = 4/3 = 1.333
Two solutions were found :
- x = 4/3 = 1.333
- x = -4/3 = -1.333
How did we do?
Please leave us feedback.