How to Square a Binomial: A Simple Guide

Squaring Binomials: A Simple Guide

In algebra, squaring a binomial is a common operation that involves multiplying a binomial by itself. A binomial is an algebraic expression with two terms, typically separated by an addition or subtraction sign. For example, (x + 2) is a binomial.

To square a binomial, we use the distributive property, also known as the FOIL method. FOIL stands for First, Outer, Inner, Last, which helps us remember the order of multiplication:

• First: Multiply the first terms of each binomial.
• Outer: Multiply the outer terms of the binomials.
• Inner: Multiply the inner terms of the binomials.
• Last: Multiply the last terms of each binomial.

Let’s illustrate this with an example:

Example: Squaring (x + 3)

1. First: (x) * (x) = x²

2. Outer: (x) * (3) = 3x

3. Inner: (3) * (x) = 3x

4. Last: (3) * (3) = 9

Now, combine the terms:

x² + 3x + 3x + 9

Simplify by combining like terms:

x² + 6x + 9

Therefore, (x + 3)² = x² + 6x + 9

General Formula

The general formula for squaring a binomial is:

(a + b)² = a² + 2ab + b²

This formula can be derived using the FOIL method, and it applies to all binomials.

Practice Problems

Here are some practice problems to test your understanding:

1. (x – 2)²
2. (2y + 5)²
3. (3a – 4b)²

Remember to use the FOIL method or the general formula to solve these problems.

Conclusion

Squaring a binomial is a fundamental concept in algebra. By understanding the distributive property and the FOIL method, you can easily square any binomial and simplify the resulting expression. This skill is essential for solving various mathematical problems and understanding more complex algebraic concepts.