Algebra

##### Related Lessons

- Adding and Subtracting Scientific Notation
- Adding Fractions
- Algebra Calculators
- Arithmetic Sequence
- Average Rate of Change
- Change of Base Formula
- Cm to M
- Commutative Property of Addition
- Completing the Square
- Cross Product Calculator
- Determinant Calculator
- Determinant of a Matrix
- Difference of Squares
- Discriminant
- Divisibility Rule for 7
- Dot Product Calculator
- Eigenvalue Calculator
- Eigenvector Calculator
- Equation of a Circle
- Even Numbers
- Exponent Rules
- Factorial Calculator
- Fractional Exponents
- How to Find the Median
- Interval Notation
- Matrix Addition
- Matrix Subtraction
- Midpoint Formula
- Multiplying Negative Numbers
- Negative Exponents
- Odd Numbers
- One to One Function
- Partial Fraction Decomposition Calculator
- Point Slope Form
- Properties of Multiplication
- Rationalize the Denominator
- Rectangular to Polar Calculator
- Reflexive Property
- Round to the Nearest Tenth
- RREF Calculator
- Slope Calculator
- Slope Intercept Form
- Standard Form
- Summation Calculator
- Vertex Form

Tutors/teachers:

# Difference of Squares

#### Lesson Contents

## The Difference of Squares Pattern

There are special patterns that some polynomials follow. **The difference of squares pattern is when a polynomial is made up of a square minus another square.** This pattern allows us to easily factor the polynomial. The formula is given as:*a ^{2} – b^{2} = (a + b)(a – b)*

Where *a* and *b* may be any algebraic expression. For example, *a* could be a variable such as “y”, and *b* could be a number such as “5”. Or, *a* could be a more complicated expression such as “2x^{3}“. The difference of squares pattern can be used for any set of algebraic expressions.

### When to use the Difference of Squares

The difference of squares pattern comes in handy when we must factor a polynomial to find the roots/zeros or to simplify it. For example, we might be tasked with finding the roots/zeros of the equation y = x^{2} – 9.

We can use the difference of squares to factor the right-hand side of the equation and then find the roots/zeroes. Applying the difference of squares pattern to x^{2} – 9 gives us (x + 3)(x – 3). Using this factored form, we can determine that the roots/zeros are x = -3 and x = 3.

### Example Problems

Problem 1:

Using the difference of squares pattern, factor the polynomial x^{2} – 49.

Solution:

1.) Let’s set a = x and b = 7 because a^{2} = x^{2} and b^{2} = 49.

2.) Applying the pattern (a + b)(a – b), we get (x + 7)(x – 7).**The factored form of the polynomial x ^{2} – 49 is (x + 7)(x – 7).**

Problem 2:

Find the x-intercepts of y = 4x^{4} – 64.

Solution:

1.) We find the x-intercepts by setting y = 0. This gives us 0 = 4x^{4} – 64.

2.) We must now find the zeroes of the expression 4x^{4} – 64. The expression is a difference of squares binomial.

3.) Applying the formula, we get:

a^{2} – b^{2} = (a + b)(a – b)

4x^{4} – 64 = (2x^{2} + 8)(2x^{2} – 8)

4.) Now that it’s in factored form, we can find the zeroes. (2x^{2} + 8)(2x^{2} – 8) has zeroes at x = 2 and x = -2.**The x-intercepts are located at x = 2 and x = -2.**

Result :

Worksheet 1

Download.pdf

Cheat sheet

Download.pdf