Binomials are expressions that consist of two terms connected with either an addition or subtraction sign. Understanding how to square binomials is a fundamental concept in algebra and can be applied in various mathematical and real-world scenarios. In this blog post, we will walk you through the step-by-step process of calculating the squares of binomials.

What is a binomial?

A binomial is a mathematical expression that contains two terms connected by addition or subtraction. It follows the general form:

(a ± b)2

Here, ‘a’ and ‘b’ are the terms, and the ± symbol represents either addition or subtraction. To find the square of this binomial, we utilize a specific algebraic method known as the FOIL method.

What is the FOIL method?

The FOIL method is an acronym that stands for First, Outer, Inner, and Last. It provides a systematic approach to multiplying two binomials. Let’s break down the steps involved:

  1. Multiply the first terms of both binomials.
  2. Multiply the outer terms.
  3. Multiply the inner terms.
  4. Multiply the last terms of both binomials.

Once these multiplications are complete, combine the like terms to simplify the expression further.

Step-by-step process for calculating the square of a binomial:

  1. Step 1: Begin with a binomial expression in the form (a ± b)2.
  2. Step 2: Apply the FOIL method to multiply the binomial by itself:

    (a ± b) × (a ± b)

    = a × a ± a × b ± b × a ± b × b

  3. Step 3: Simplify the expression by combining like terms:

    = a2 ± 2ab + b2

  4. Step 4: The result is the square of the binomial:

(a ± b)2 = a2 ± 2ab + b2

Example:

Let’s illustrate this process with an example:

Find the square of the binomial (2x + 3y).

Following the steps discussed earlier, we perform the corresponding multiplications:

(2x + 3y) × (2x + 3y)

= (2x) × (2x) + (2x) × (3y) + (3y) × (2x) + (3y) × (3y)

= 4x2 + 6xy + 6xy + 9y2

= 4x2 + 12xy + 9y2

Therefore, the square of the binomial (2x + 3y) is 4x2 + 12xy + 9y2.

Calculating the squares of binomials is an essential skill in algebra. By implementing the FOIL method and simplifying the result, you can easily find the square of any given binomial expression. Remember to pay close attention to signs and combine like terms to obtain the final answer. Practice this method and try various examples to enhance your understanding. Happy calculating!

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