Understanding the Square of a Binomial Formula

Oct 13, 2025 by windailys.com 118 views

Simplify $(5m - 4)^2$ using the square of a binomial formula

In algebra, the square of a binomial formula is a powerful tool used to simplify expressions that involve the square of a binomial. The formula states that $(a - b)^2 = a^2 - 2ab + b^2$ . In this article, we will use this formula to simplify the expression $(5m - 4)^2$ .

Understanding the Square of a Binomial Formula

The square of a binomial formula is a fundamental concept in algebra that allows us to simplify expressions that involve the square of a binomial. The formula is as follows:

$(a - b)^2 = a^2 - 2ab + b^2$

This formula can be used to simplify expressions that involve the square of a binomial by substituting the values of $a$ and $b$ into the formula.

Simplifying $(5m - 4)^2$ using the Square of a Binomial Formula

To simplify the expression $(5m - 4)^2$ , we can use the square of a binomial formula. We will substitute $a = 5m$ and $b = 4$ into the formula.

$(5m - 4)^2 = (5m)^2 - 2(5m)(4) + 4^2$

Now, we can simplify the expression by evaluating the terms.

$(5m)^2 = 25m^2$

$2(5m)(4) = 40m$

$4^2 = 16$

Substituting these values into the expression, we get:

$(5m - 4)^2 = 25m^2 - 40m + 16$

In this article, we used the square of a binomial formula to simplify the expression $(5m - 4)^2$ . We substituted $a = 5m$ and $b = 4$ into the formula and evaluated the terms to get the simplified expression. The correct answer is:

$25m^2 - 40m + 16$

This is the correct answer because it matches the expression we obtained by using the square of a binomial formula.

Let's compare the options to see which one matches the expression we obtained.

Option A: $25m^2 + 40m + 16$
Option B: $5m^2 - 40m + 4$
Option C: $25m^2 - 40m + 16$
Option D: $5m^2 - 20m - 4$

Only option C matches the expression we obtained.

The final answer is:

C) $25m^2 - 40m + 16$

This is the correct answer because it matches the expression we obtained by using the square of a binomial formula.
Simplify $(5m - 4)^2$ using the square of a binomial formula: Q&A

In our previous article, we used the square of a binomial formula to simplify the expression $(5m - 4)^2$ . In this article, we will answer some frequently asked questions about the square of a binomial formula and its application to simplify expressions.

Q: What is the square of a binomial formula?

A: The square of a binomial formula is a fundamental concept in algebra that allows us to simplify expressions that involve the square of a binomial. The formula is as follows:

$(a - b)^2 = a^2 - 2ab + b^2$

Q: How do I use the square of a binomial formula to simplify expressions?

A: To use the square of a binomial formula to simplify expressions, you need to substitute the values of $a$ and $b$ into the formula. For example, if you want to simplify the expression $(5m - 4)^2$ , you would substitute $a = 5m$ and $b = 4$ into the formula.

Q: What are the steps to simplify an expression using the square of a binomial formula?

A: The steps to simplify an expression using the square of a binomial formula are as follows:

Substitute the values of $a$ and $b$ into the formula.
Evaluate the terms in the expression.
Simplify the expression by combining like terms.

Q: Can I use the square of a binomial formula to simplify expressions with negative numbers?

A: Yes, you can use the square of a binomial formula to simplify expressions with negative numbers. For example, if you want to simplify the expression $(-5m - 4)^2$ , you would substitute $a = -5m$ and $b = 4$ into the formula.

Q: What are some common mistakes to avoid when using the square of a binomial formula?

A: Some common mistakes to avoid when using the square of a binomial formula include:

Not substituting the values of $a$ and $b$ into the formula correctly.
Not evaluating the terms in the expression correctly.
Not simplifying the expression by combining like terms.

Q: Can I use the square of a binomial formula to simplify expressions with variables?

A: Yes, you can use the square of a binomial formula to simplify expressions with variables. For example, if you want to simplify the expression $(2x + 3)^2$ , you would substitute $a = 2x$ and $b = 3$ into the formula.

Q: What are some real-world applications of the square of a binomial formula?

A: The square of a binomial formula has many real-world applications, including:

Simplifying expressions in algebra and calculus.
Solving equations and inequalities.
Modeling real-world phenomena, such as population growth and motion.

In this article, we answered some frequently asked questions about the square of a binomial formula and its application to simplify expressions. We hope that this article has been helpful in clarifying any doubts you may have had about the square of a binomial formula.

Make sure to substitute the values of $a$ and $b$ into the formula correctly.
Evaluate the terms in the expression correctly.
Simplify the expression by combining like terms.
Practice using the square of a binomial formula to simplify expressions with variables and negative numbers.

By following these tips, you will be able to use the square of a binomial formula to simplify expressions with confidence.