Subtract:$\[ \left(7z^2 + 4v\right) - \left(-13z^2\right) \\]Your Answer Should Be In Simplest Terms.Enter The Correct Answer.

by ADMIN 127 views

=====================================================

Understanding the Basics of Algebraic Expressions

Algebraic expressions are a fundamental concept in mathematics, and they play a crucial role in solving various mathematical problems. In this article, we will focus on simplifying algebraic expressions, specifically the subtraction of two expressions. We will use the given expression as an example and break it down into simpler terms.

The Given Expression

The given expression is:

(7z2+4v)−(−13z2)\left(7z^2 + 4v\right) - \left(-13z^2\right)

Distributive Property

To simplify the given expression, we will use the distributive property, which states that for any real numbers a, b, and c:

a(b + c) = ab + ac

Applying the Distributive Property

We will apply the distributive property to the given expression by distributing the negative sign to the terms inside the second set of parentheses:

(7z2+4v)−(−13z2)\left(7z^2 + 4v\right) - \left(-13z^2\right)

= (7z2+4v)+13z2\left(7z^2 + 4v\right) + 13z^2

Combining Like Terms

Now that we have distributed the negative sign, we can combine like terms. Like terms are terms that have the same variable raised to the same power. In this case, we have two terms with the variable z^2:

7z2+13z27z^2 + 13z^2

Simplifying the Expression

To simplify the expression, we will combine the two terms with the variable z^2:

7z2+13z2=20z27z^2 + 13z^2 = 20z^2

Final Answer

The simplified expression is:

20z2+4v20z^2 + 4v

Conclusion

In this article, we have simplified the given algebraic expression using the distributive property and combining like terms. We have shown that the expression can be simplified to:

20z2+4v20z^2 + 4v

This is the simplest form of the expression, and it is the final answer.

Frequently Asked Questions

Q: What is the distributive property?

A: The distributive property is a mathematical concept that states that for any real numbers a, b, and c:

a(b + c) = ab + ac

Q: How do I combine like terms?

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

Q: What is the final answer?

A: The final answer is 20z2+4v20z^2 + 4v.

Additional Resources

For more information on algebraic expressions and simplifying them, you can refer to the following resources:

  • Khan Academy: Algebraic Expressions
  • Mathway: Simplifying Algebraic Expressions
  • Wolfram Alpha: Algebraic Expressions

Final Thoughts

Simplifying algebraic expressions is an essential skill in mathematics, and it requires a good understanding of the distributive property and combining like terms. By following the steps outlined in this article, you can simplify any algebraic expression and arrive at the final answer.

=====================================================

Understanding Algebraic Expressions

Algebraic expressions are a fundamental concept in mathematics, and they play a crucial role in solving various mathematical problems. In this article, we will answer some frequently asked questions about 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 the basic components of an algebraic expression?

A: The basic components of an algebraic expression are:

  • Variables: These are letters or symbols that represent unknown values.
  • Constants: These are numbers that do not change value.
  • Mathematical operations: These are the operations that can be performed on variables and constants, such as addition, subtraction, multiplication, and division.

Q: How do I simplify an algebraic expression?

A: To simplify an algebraic expression, you need to follow these steps:

  1. Distribute the negative sign to the terms inside the second set of parentheses.
  2. Combine like terms by adding or subtracting the coefficients of the terms with the same variable raised to the same power.
  3. Simplify the expression by combining the terms.

Q: What is the distributive property?

A: The distributive property is a mathematical concept that states that for any real numbers a, b, and c:

a(b + c) = ab + ac

Q: How do I combine like terms?

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

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

A: A variable is a letter or symbol that represents an unknown value, while a constant is a number that does not change value.

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 is the order of operations?

A: The order of operations is a set of rules that dictates the order in which mathematical operations should be performed. The order of operations is:

  1. Parentheses: Evaluate expressions inside parentheses first.
  2. Exponents: Evaluate any exponential expressions next.
  3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
  4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: How do I simplify a fraction?

A: To simplify a fraction, you need to divide the numerator and denominator by their greatest common divisor (GCD).

Q: What is the greatest common divisor (GCD)?

A: The greatest common divisor (GCD) is the largest number that divides two or more numbers without leaving a remainder.

Q: How do I simplify a rational expression?

A: To simplify a rational expression, you need to follow these steps:

  1. Factor the numerator and denominator.
  2. Cancel out any common factors.
  3. Simplify the expression.

Q: What is a rational expression?

A: A rational expression is a mathematical expression that consists of a fraction of two polynomials.

Q: How do I add or subtract rational expressions?

A: To add or subtract rational expressions, you need to follow these steps:

  1. Factor the numerator and denominator of each expression.
  2. Cancel out any common factors.
  3. Add or subtract the expressions.

Q: What is the final answer?

A: The final answer is 20z2+4v20z^2 + 4v.

Additional Resources

For more information on algebraic expressions and simplifying them, you can refer to the following resources:

  • Khan Academy: Algebraic Expressions
  • Mathway: Simplifying Algebraic Expressions
  • Wolfram Alpha: Algebraic Expressions

Final Thoughts

Algebraic expressions are a fundamental concept in mathematics, and they play a crucial role in solving various mathematical problems. By understanding the basics of algebraic expressions and following the steps outlined in this article, you can simplify any algebraic expression and arrive at the final answer.