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Chapter 5: Problem 105

Explain how to square a binomial sum. Give an example with your explanation.

Short Answer

Expert verified
To square a binomial sum, use the formula \((a+b)^2 = a^2 + 2ab + b^2\). For example, the square of \((3x + 4y)\) is \( 9x^2 + 24xy + 16y^2 \).

Step by step solution

01

Recognize the binomial

A binomial is simply an algebraic expression consisting of two terms. For instance, \(a + b\) is a binomial.
02

Apply the binomial square formula

The formula for the square of a binomial \((a + b)^2\) is \(a^2 + 2ab + b^2\). This formula is applied by multiplying and adding the terms according to the formula.
03

Work through an example

Let's take the binomial \((3x + 4y)\) and apply the formula. The result is \( (3x)^2 + 2 * 3x * 4y + (4y)^2 \), which simplifies to \( 9x^2 + 24xy + 16y^2 \).

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