Simplify The Expression:${ -(-3x)(-2x) }$

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Introduction

In mathematics, simplifying expressions is a crucial skill that helps us solve problems efficiently. When dealing with algebraic expressions, we often encounter negative signs, parentheses, and variables. In this article, we will focus on simplifying the given expression: −(−3x)(−2x)-(-3x)(-2x). We will break down the steps involved in simplifying this expression and provide a clear understanding of the mathematical concepts involved.

Understanding the Expression

The given expression is −(−3x)(−2x)-(-3x)(-2x). Let's analyze it step by step:

  • The expression contains three negative signs: two negative signs in front of the parentheses and one negative sign inside the parentheses.
  • The expression also contains two variables: xx and −x-x.
  • The expression is enclosed in parentheses, which indicates that the operations inside the parentheses should be performed first.

Step 1: Remove the Negative Signs Inside the Parentheses

When we have a negative sign in front of a variable, it means that the variable is being multiplied by −1-1. In this case, we have −3x-3x and −2x-2x. To simplify the expression, we can remove the negative signs inside the parentheses by multiplying the variables by −1-1.

-(-3x) = 3x
-(-2x) = 2x

Step 2: Multiply the Variables

Now that we have removed the negative signs inside the parentheses, we can multiply the variables together.

(3x)(2x) = 6x^2

Step 3: Simplify the Expression

Now that we have multiplied the variables together, we can simplify the expression by combining the terms.

-(-3x)(-2x) = -6x^2

Conclusion

In this article, we simplified the expression −(−3x)(−2x)-(-3x)(-2x) by removing the negative signs inside the parentheses, multiplying the variables together, and simplifying the expression. We hope that this article has provided a clear understanding of the mathematical concepts involved in simplifying algebraic expressions.

Frequently Asked Questions

Q: What is the difference between a negative sign and a positive sign?

A: A negative sign indicates that the variable is being multiplied by −1-1, while a positive sign indicates that the variable is being multiplied by 11.

Q: How do I simplify an expression with multiple negative signs?

A: To simplify an expression with multiple negative signs, you can remove the negative signs inside the parentheses by multiplying the variables by −1-1, and then multiply the variables together.

Q: What is the order of operations in mathematics?

A: The order of operations in mathematics 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.

Final Thoughts

Simplifying expressions is an essential skill in mathematics that helps us solve problems efficiently. By understanding the mathematical concepts involved in simplifying algebraic expressions, we can tackle complex problems with confidence. We hope that this article has provided a clear understanding of the steps involved in simplifying the expression −(−3x)(−2x)-(-3x)(-2x).

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Introduction

In our previous article, we simplified the expression −(−3x)(−2x)-(-3x)(-2x) by removing the negative signs inside the parentheses, multiplying the variables together, and simplifying the expression. In this article, we will provide a Q&A section to address some common questions and concerns related to simplifying algebraic expressions.

Q&A

Q: What is the difference between a negative sign and a positive sign?

A: A negative sign indicates that the variable is being multiplied by −1-1, while a positive sign indicates that the variable is being multiplied by 11.

Q: How do I simplify an expression with multiple negative signs?

A: To simplify an expression with multiple negative signs, you can remove the negative signs inside the parentheses by multiplying the variables by −1-1, and then multiply the variables together.

Q: What is the order of operations in mathematics?

A: The order of operations in mathematics 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 an expression with variables and constants?

A: To simplify an expression with variables and constants, you can combine like terms by adding or subtracting the coefficients of the variables.

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

A: A coefficient is a number that is multiplied by a variable, while a variable is a letter or symbol that represents a value.

Q: How do I simplify an expression with fractions?

A: To simplify an expression with fractions, you can multiply the numerator and denominator by the same value to eliminate the fraction.

Q: What is the difference between a rational expression and an irrational expression?

A: A rational expression is an expression that can be written as a fraction, while an irrational expression is an expression that cannot be written as a fraction.

Q: How do I simplify an expression with absolute values?

A: To simplify an expression with absolute values, you can remove the absolute value signs by considering the positive and negative cases separately.

Examples

Example 1: Simplify the expression −(−2x)(−3x)-(-2x)(-3x)

-(-2x)(-3x) = -6x^2

Example 2: Simplify the expression (−4x)(−2x)(-4x)(-2x)

(-4x)(-2x) = 8x^2

Example 3: Simplify the expression (−3x)(−2x)+4x(-3x)(-2x) + 4x

(-3x)(-2x) + 4x = 6x^2 + 4x

Conclusion

In this article, we provided a Q&A section to address some common questions and concerns related to simplifying algebraic expressions. We hope that this article has provided a clear understanding of the mathematical concepts involved in simplifying expressions with variables, constants, fractions, and absolute values.

Frequently Asked Questions

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

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

Q: How do I simplify an expression with exponents?

A: To simplify an expression with exponents, you can use the rules of exponents to combine like terms.

Q: What is the difference between a rational expression and an irrational expression?

A: A rational expression is an expression that can be written as a fraction, while an irrational expression is an expression that cannot be written as a fraction.

Q: How do I simplify an expression with absolute values?

A: To simplify an expression with absolute values, you can remove the absolute value signs by considering the positive and negative cases separately.

Final Thoughts

Simplifying expressions is an essential skill in mathematics that helps us solve problems efficiently. By understanding the mathematical concepts involved in simplifying algebraic expressions, we can tackle complex problems with confidence. We hope that this article has provided a clear understanding of the steps involved in simplifying expressions with variables, constants, fractions, and absolute values.