Simplify The Expression: ( 2 X − 11 X 2 + 14 ) + ( 7 X 2 − X + 3 (2x - 11x^2 + 14) + (7x^2 - X + 3 ( 2 X − 11 X 2 + 14 ) + ( 7 X 2 − X + 3 ]

$$

Introduction

Simplifying algebraic expressions is a crucial skill in mathematics, and it's essential to understand the rules and techniques involved. In this article, we will focus on simplifying the given expression: $(2x - 11x^2 + 14) + (7x^2 - x + 3)$. We will break down the expression into smaller parts, combine like terms, and simplify the resulting expression.

Understanding the Expression

The given expression is a combination of two separate expressions: $(2x - 11x^2 + 14)$ and $(7x^2 - x + 3)$. To simplify the expression, we need to combine like terms, which means combining terms that have the same variable and exponent.

Combining Like Terms

To combine like terms, we need to identify the terms that have the same variable and exponent. In this case, we have the following terms:

• $2x$ and $-x$ (both have the variable $x$ and an exponent of 1)
• $-11x^2$ and $7x^2$ (both have the variable $x$ and an exponent of 2)
• $14$ and $3$ (both are constants)

Simplifying the Expression

Now that we have identified the like terms, we can combine them to simplify the expression. We will start by combining the terms with the same variable and exponent.

Combining Terms with the Variable $x$

We have two terms with the variable $x$: $2x$ and $-x$. To combine these terms, we add their coefficients:

$2x + (-x) = (2 - 1)x = x$

So, the combined term is $x$.

Combining Terms with the Variable $x^2$

We have two terms with the variable $x^2$: $-11x^2$ and $7x^2$. To combine these terms, we add their coefficients:

$-11x^2 + 7x^2 = (-11 + 7)x^2 = -4x^2$

So, the combined term is $-4x^2$.

Combining Constants

We have two constants: $14$ and $3$. To combine these constants, we add them:

$14 + 3 = 17$

So, the combined constant is $17$.

Final Simplified Expression

Now that we have combined all the like terms, we can write the final simplified expression:

$x - 4x^2 + 17$

Conclusion

Simplifying algebraic expressions is an essential skill in mathematics, and it's crucial to understand the rules and techniques involved. In this article, we simplified the given expression: $(2x - 11x^2 + 14) + (7x^2 - x + 3)$ by combining like terms and simplifying the resulting expression. We identified the like terms, combined them, and wrote the final simplified expression. This technique is essential in solving algebraic equations and inequalities, and it's a fundamental concept in mathematics.

Tips and Tricks

• When simplifying algebraic expressions, it's essential to identify like terms and combine them.
• Use the distributive property to expand expressions and combine like terms.
• Simplify expressions by combining constants and variables separately.
• Use parentheses to group terms and simplify expressions.

Common Mistakes

• Failing to identify like terms and combine them.
• Not using the distributive property to expand expressions.
• Simplifying expressions by combining variables and constants together.
• Not using parentheses to group terms and simplify expressions.

Real-World Applications

Simplifying algebraic expressions has numerous real-world applications, including:

• Solving algebraic equations and inequalities.
• Modeling real-world problems using algebraic expressions.
• Simplifying complex expressions in physics, engineering, and computer science.
• Solving optimization problems using algebraic expressions.

Final Thoughts

Simplifying algebraic expressions is a fundamental concept in mathematics, and it's essential to understand the rules and techniques involved. By following the steps outlined in this article, you can simplify complex expressions and solve algebraic equations and inequalities. Remember to identify like terms, combine them, and simplify the resulting expression. With practice and patience, you can master the art of simplifying algebraic expressions and apply it to real-world problems.

$$

Introduction

In our previous article, we simplified the given expression: $(2x - 11x^2 + 14) + (7x^2 - x + 3)$ by combining like terms and simplifying the resulting expression. In this article, we will answer some frequently asked questions (FAQs) related to simplifying algebraic expressions.

Q&A

Q1: What are like terms in algebra?

A1: Like terms are terms that have the same variable and exponent. For example, $2x$ and $-x$ are like terms because they both have the variable $x$ and an exponent of 1.

Q2: How do I identify like terms in an expression?

A2: To identify like terms, look for terms that have the same variable and exponent. You can also use the distributive property to expand expressions and combine like terms.

Q3: What is the distributive property in algebra?

A3: The distributive property is a rule that allows you to expand expressions by multiplying each term inside the parentheses by the term outside the parentheses. For example, $a(b + c) = ab + ac$.

Q4: How do I simplify an expression with multiple variables?

A4: To simplify an expression with multiple variables, identify like terms and combine them. You can also use the distributive property to expand expressions and combine like terms.

Q5: What is the order of operations in algebra?

A5: The order of operations in algebra is:

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

Q6: How do I simplify an expression with fractions?

A6: To simplify an expression with fractions, find a common denominator and combine the fractions. You can also use the distributive property to expand expressions and combine like terms.

Q7: What is the difference between a variable and a constant in algebra?

A7: A variable is a letter or symbol that represents a value that can change. A constant is a value that does not change.

Q8: How do I simplify an expression with negative numbers?

A8: To simplify an expression with negative numbers, combine like terms and simplify the resulting expression. You can also use the distributive property to expand expressions and combine like terms.

Q9: What is the purpose of simplifying algebraic expressions?

A9: The purpose of simplifying algebraic expressions is to make them easier to work with and to solve equations and inequalities.

Q10: How do I know if an expression is simplified?

A10: An expression is simplified when there are no like terms left to combine. You can also use the distributive property to expand expressions and combine like terms to check if an expression is simplified.

Conclusion

Simplifying algebraic expressions is an essential skill in mathematics, and it's crucial to understand the rules and techniques involved. By following the steps outlined in this article and answering the FAQs, you can simplify complex expressions and solve algebraic equations and inequalities. Remember to identify like terms, combine them, and simplify the resulting expression. With practice and patience, you can master the art of simplifying algebraic expressions and apply it to real-world problems.

Tips and Tricks

• When simplifying algebraic expressions, it's essential to identify like terms and combine them.
• Use the distributive property to expand expressions and combine like terms.
• Simplify expressions by combining constants and variables separately.
• Use parentheses to group terms and simplify expressions.

Common Mistakes

• Failing to identify like terms and combine them.
• Not using the distributive property to expand expressions.
• Simplifying expressions by combining variables and constants together.
• Not using parentheses to group terms and simplify expressions.

Real-World Applications

Simplifying algebraic expressions has numerous real-world applications, including:

• Solving algebraic equations and inequalities.
• Modeling real-world problems using algebraic expressions.
• Simplifying complex expressions in physics, engineering, and computer science.
• Solving optimization problems using algebraic expressions.

Final Thoughts

Simplifying algebraic expressions is a fundamental concept in mathematics, and it's essential to understand the rules and techniques involved. By following the steps outlined in this article and answering the FAQs, you can simplify complex expressions and solve algebraic equations and inequalities. Remember to identify like terms, combine them, and simplify the resulting expression. With practice and patience, you can master the art of simplifying algebraic expressions and apply it to real-world problems.