Select All The Coefficients Of The Product \[$(5y - 3)^2\$\].A. -30 B. -6 C. 9 D. 10 E. 25

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Introduction

In algebra, expanding and simplifying expressions is a crucial skill that helps us solve equations and manipulate variables. When we expand an expression, we multiply out the terms to get a simpler form. In this article, we will focus on expanding the expression {(5y - 3)^2$}$ and selecting the coefficients of the resulting terms.

What are Coefficients?

Before we dive into the expansion, let's quickly review what coefficients are. A coefficient is a number that is multiplied by a variable or a group of variables in an algebraic expression. For example, in the expression ${2x + 3y\$}, the coefficient of {x$}$ is 2, and the coefficient of {y$}$ is 3.

Expanding the Expression

To expand the expression {(5y - 3)^2$}$, we will use the formula for squaring a binomial:

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

In this case, {a = 5y$}$ and {b = 3$}$. Plugging these values into the formula, we get:

{(5y - 3)^2 = (5y)^2 - 2(5y)(3) + 3^2$}$

Expanding the terms, we get:

{(5y)^2 = 25y^2$}$

{-2(5y)(3) = -30y$}$

${3^2 = 9\$}

So, the expanded expression is:

${25y^2 - 30y + 9\$}

Selecting the Coefficients

Now that we have expanded the expression, we need to select the coefficients of the resulting terms. The coefficients are the numbers that are multiplied by the variables. In this case, the coefficients are:

  • The coefficient of {y^2$}$ is 25.
  • The coefficient of {y$}$ is -30.
  • The constant term is 9.

Answer

Based on the expanded expression, the correct answer is:

  • A. -30 (coefficient of {y$}$)
  • C. 9 (constant term)

Conclusion

Q: What is the formula for squaring a binomial?

A: The formula for squaring a binomial is {(a - b)^2 = a^2 - 2ab + b^2$}$.

Q: How do I expand the expression {(5y - 3)^2$}$?

A: To expand the expression {(5y - 3)^2$}$, you can use the formula for squaring a binomial. Plug in {a = 5y$}$ and {b = 3$}$ into the formula and expand the terms.

Q: What are the coefficients of the expression ${25y^2 - 30y + 9\$}?

A: The coefficients of the expression ${25y^2 - 30y + 9\$} are:

  • The coefficient of {y^2$}$ is 25.
  • The coefficient of {y$}$ is -30.
  • The constant term is 9.

Q: How do I select the correct answer from the options?

A: To select the correct answer from the options, identify the coefficients of the expression and match them with the options. In this case, the correct answers are:

  • A. -30 (coefficient of {y$}$)
  • C. 9 (constant term)

Q: What is the importance of selecting coefficients in algebra?

A: Selecting coefficients is an important skill in algebra because it helps you to:

  • Simplify expressions
  • Solve equations
  • Manipulate variables
  • Identify patterns and relationships between variables

Q: Can I use the formula for squaring a binomial to expand other expressions?

A: Yes, you can use the formula for squaring a binomial to expand other expressions. The formula is a general rule that can be applied to any binomial expression.

Q: What if I get stuck while expanding an expression?

A: If you get stuck while expanding an expression, try breaking it down into smaller parts and using the formula for squaring a binomial. You can also use algebraic properties and rules to simplify the expression.

Q: How can I practice expanding and selecting coefficients?

A: You can practice expanding and selecting coefficients by:

  • Working through algebraic exercises and problems
  • Using online resources and practice tests
  • Asking a teacher or tutor for help
  • Joining a study group or online community to discuss algebraic concepts

Conclusion

In this article, we answered frequently asked questions on expanding and selecting coefficients. We covered topics such as the formula for squaring a binomial, expanding expressions, selecting coefficients, and practicing algebraic skills. We hope this article has been helpful in clarifying any doubts you may have had on these topics.