Solving a Quadratic Equation Using a Difference of Squares
(KS4, Year 10)
- x2 = x × x (x squared).
- 9 = 32 = 3 × 3 (3 squared).
How to Factor a Quadratic Equation Using a Difference of Squares
A quadratic equation in the form of a difference of squares can be factored into two brackets:How to Solve Quadratic Equations Using a Difference of Squares
Solving a quadratic equation using a difference of squares is easy.Question
Solve the quadratic equation shown below using a difference of squares.Step-by-Step:
1
Rewrite the quadratic equation as a difference of squares.
In our example, 9 = 3 × 3 = 32.
x2 − 9 = x2 − 32
2
Compare the difference of squares with the formula to find a.
a = 3
3
Use the formula to factor the difference of squares:
x2 − a2 = (x + a)(x − a)
4
Substitute a = 3 into the formula.
x2 − 32 = (x + 3)(x − 3)
5
Rewrite the quadratic equation.
6
Equate the first bracket to 0 and solve to find x.
x + 3 = 0 ⇒ x = −3
7
Equate the second bracket to 0 and solve to find x.
x − 3 = 0 ⇒ x = 3
Answer:
We have factored the quadratic equation using a difference of squares: x2 − 9 = (x + 3)(x − 3) = 0. We have solved the quadratic equation: x = −3, x = 3.What Is a Difference of Squares
A difference of squares is square number (a number multiplied by itself) subtracted from another square number. An example of a difference of squares using numbers is: In general, we can use symbols instead of numbers: This can be factored into two brackets:
a2 − b2 = (a + b)(a − b)
Factoring, Factorising
To write a quadratic equation as a product of two brackets is called 'to factor' or 'to factorise' the quadratic equation, depending on the country. The method is refered to as 'factoring' or 'factorising'.Worksheet
This test is printable and sendable