Subtract:${ 2b^2 - \left(-10b^2 - 4d\right) }$Your Answer Should Be In Simplest Terms.Enter The Correct Answer.

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In mathematics, algebraic expressions are a fundamental concept that helps us solve equations and manipulate variables. One of the essential skills in algebra is simplifying expressions, which involves combining like terms and eliminating unnecessary components. In this article, we will focus on simplifying a specific algebraic expression, which involves subtracting one expression from another.

Understanding the Expression

The given expression is 2b2−(−10b2−4d)2b^2 - \left(-10b^2 - 4d\right). To simplify this expression, we need to follow the order of operations (PEMDAS) and apply the rules of algebra. The expression involves two main components: 2b22b^2 and (−10b2−4d)\left(-10b^2 - 4d\right). Our goal is to simplify this expression by combining like terms and eliminating any unnecessary components.

Distributive Property

The first step in simplifying the expression is to apply the distributive property. The distributive property states that for any real numbers aa, bb, and cc, a(b+c)=ab+aca(b + c) = ab + ac. In our expression, we have a negative sign in front of the second term, which means we need to distribute the negative sign to both terms inside the parentheses.

2b^2 - (-10b^2 - 4d) = 2b^2 + 10b^2 + 4d

Combining Like Terms

Now that we have applied the distributive property, we can combine like terms. Like terms are terms that have the same variable raised to the same power. In our expression, we have two terms with the variable b2b^2: 2b22b^2 and 10b210b^2. We can combine these terms by adding their coefficients.

2b^2 + 10b^2 = 12b^2

Final Simplified Expression

Now that we have combined like terms, we can simplify the expression further by eliminating any unnecessary components. In our expression, we have the term 4d4d, which is not related to the variable b2b^2. We can leave this term as it is, since it is not a like term with any other term in the expression.

The final simplified expression is:

12b^2 + 4d

Conclusion

Simplifying algebraic expressions is an essential skill in mathematics, and it requires a deep understanding of the rules of algebra. By applying the distributive property and combining like terms, we can simplify complex expressions and make them easier to work with. In this article, we have simplified the expression 2b2−(−10b2−4d)2b^2 - \left(-10b^2 - 4d\right), which involves subtracting one expression from another. The final simplified expression is 12b2+4d12b^2 + 4d.

Frequently Asked Questions

Q: What is the distributive property?

A: The distributive property is a rule in algebra that states that for any real numbers aa, bb, and cc, a(b+c)=ab+aca(b + c) = ab + ac.

Q: How do I combine like terms?

A: To combine like terms, you need to add the coefficients of the terms with the same variable raised to the same power.

Q: What is the final simplified expression?

A: The final simplified expression is 12b2+4d12b^2 + 4d.

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In our previous article, we discussed simplifying algebraic expressions, which is an essential skill in mathematics. However, we know that algebra can be a challenging subject, and many students struggle to understand the concepts. In this article, we will provide answers to some of the most frequently asked questions about algebraic expressions.

Q&A: Algebraic Expressions

Q: What is an algebraic expression?

A: An algebraic expression is a mathematical expression that consists of variables, constants, and mathematical operations. It is a way to represent a mathematical relationship between variables and constants.

Q: What are like terms?

A: Like terms are terms that have the same variable raised to the same power. For example, 2x22x^2 and 5x25x^2 are like terms because they both have the variable xx raised to the power of 2.

Q: How do I simplify an algebraic expression?

A: To simplify an algebraic expression, you need to follow the order of operations (PEMDAS) and apply the rules of algebra. This includes combining like terms, eliminating unnecessary components, and applying the distributive property.

Q: What is the distributive property?

A: The distributive property is a rule in algebra that states that for any real numbers aa, bb, and cc, a(b+c)=ab+aca(b + c) = ab + ac. This means that you can distribute a single term to multiple terms inside parentheses.

Q: How do I combine like terms?

A: To combine like terms, you need to add the coefficients of the terms with the same variable raised to the same power. For example, 2x2+5x2=7x22x^2 + 5x^2 = 7x^2.

Q: What is the difference between an algebraic expression and an equation?

A: An algebraic expression is a mathematical expression that consists of variables, constants, and mathematical operations. An equation is a statement that says two expressions are equal. For example, 2x2+3x−4=02x^2 + 3x - 4 = 0 is an equation, while 2x2+3x−42x^2 + 3x - 4 is an algebraic expression.

Q: How do I evaluate an algebraic expression?

A: To evaluate an algebraic expression, you need to substitute the values of the variables and constants into the expression and perform the mathematical operations.

Q: What are some common algebraic expressions?

A: Some common algebraic expressions include:

  • Linear expressions: ax+bax + b
  • Quadratic expressions: ax2+bx+cax^2 + bx + c
  • Polynomial expressions: anxn+an−1xn−1+…+a1x+a0a_nx^n + a_{n-1}x^{n-1} + \ldots + a_1x + a_0

Conclusion

Algebraic expressions are a fundamental concept in mathematics, and understanding them is essential for solving equations and manipulating variables. In this article, we have provided answers to some of the most frequently asked questions about algebraic expressions. We hope that this article has helped you to better understand the concepts of algebraic expressions and how to simplify them.

Frequently Asked Questions

Q: What is the order of operations?

A: The order of operations is a set of rules that tells you which operations to perform first when evaluating an expression. The order of operations is:

  1. Parentheses
  2. Exponents
  3. Multiplication and Division
  4. Addition and Subtraction

Q: What is the difference between a variable and a constant?

A: A variable is a symbol that represents a value that can change. A constant is a value that does not change.

Q: How do I simplify a complex algebraic expression?

A: To simplify a complex algebraic expression, you need to follow the order of operations and apply the rules of algebra. This includes combining like terms, eliminating unnecessary components, and applying the distributive property.

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