Q5: Simplify If Possible.a. 12 A − 7 A 12a - 7a 12 A − 7 A B. 6 A + 12 B − 7 A + 11 B 6a + 12b - 7a + 11b 6 A + 12 B − 7 A + 11 B C. 2 A 2 − 4 A 2a^2 - 4a 2 A 2 − 4 A

Mar 10, 2025 by ADMIN 167 views

**Simplifying Algebraic Expressions: A Step-by-Step Guide**

Introduction

Algebraic expressions are a fundamental concept in mathematics, and simplifying them is an essential skill for any math enthusiast. In this article, we will explore the process of simplifying algebraic expressions, focusing on the given examples: $12a - 7a$ , $6a + 12b - 7a + 11b$ , and $2a^2 - 4a$ . By the end of this article, you will have a clear understanding of how to simplify algebraic expressions and be able to apply this knowledge to various mathematical problems.

Simplifying the First Expression: $12a - 7a$

The first expression we will simplify is $12a - 7a$ . To simplify this expression, we need to combine like terms, which are terms that have the same variable raised to the same power.

12a - 7a = (12 - 7)a

By subtracting the coefficients of the like terms, we get:

(12 - 7)a = 5a

Therefore, the simplified expression is $5a$ .

Simplifying the Second Expression: $6a + 12b - 7a + 11b$

The second expression we will simplify is $6a + 12b - 7a + 11b$ . To simplify this expression, we need to combine like terms.

6a + 12b - 7a + 11b = (6 - 7)a + (12 + 11)b

By subtracting the coefficients of the like terms, we get:

(6 - 7)a + (12 + 11)b = -a + 23b

Therefore, the simplified expression is $-a + 23b$ .

Simplifying the Third Expression: $2a^2 - 4a$

The third expression we will simplify is $2a^2 - 4a$ . To simplify this expression, we need to factor out the greatest common factor (GCF) of the terms.

2a^2 - 4a = 2a(a - 2)

By factoring out the GCF, we get:

2a(a - 2) = 2a(a - 2)

Therefore, the simplified expression is $2a(a - 2)$ .

Conclusion

Simplifying algebraic expressions is an essential skill for any math enthusiast. By combining like terms and factoring out the greatest common factor, we can simplify expressions and make them easier to work with. In this article, we simplified three expressions: $12a - 7a$ , $6a + 12b - 7a + 11b$ , and $2a^2 - 4a$ . By following the steps outlined in this article, you can simplify any algebraic expression and be able to apply this knowledge to various mathematical problems.

Tips and Tricks

Always combine like terms when simplifying an expression.
Factor out the greatest common factor (GCF) of the terms to simplify the expression.
Use the distributive property to expand expressions and simplify them.
Simplify expressions by combining like terms and factoring out the GCF.

Common Mistakes to Avoid

Not combining like terms when simplifying an expression.
Not factoring out the greatest common factor (GCF) of the terms.
Not using the distributive property to expand expressions and simplify them.
Not simplifying expressions by combining like terms and factoring out the GCF.

Real-World Applications

Simplifying algebraic expressions has many real-world applications. For example:

In physics, simplifying algebraic expressions is used to describe the motion of objects and the forces acting on them.
In engineering, simplifying algebraic expressions is used to design and optimize systems.
In economics, simplifying algebraic expressions is used to model and analyze economic systems.

Final Thoughts

Q: What is the first step in simplifying an algebraic expression?

A: The first step in simplifying an algebraic expression is to combine like terms. Like terms are terms that have the same variable raised to the same power.

Q: How do I combine like terms?

A: To combine like terms, you need to add or subtract the coefficients of the like terms. For example, if you have the expression $3x + 2x$ , you can combine the like terms by adding the coefficients: $3x + 2x = (3 + 2)x = 5x$ .

Q: What is the greatest common factor (GCF)?

A: The greatest common factor (GCF) is the largest factor that divides all the terms in an expression. For example, in the expression $6a^2 + 12a$ , the GCF is $6a$ .

Q: How do I factor out the GCF?

A: To factor out the GCF, you need to divide each term in the expression by the GCF. For example, in the expression $6a^2 + 12a$ , you can factor out the GCF $6a$ by dividing each term by $6a$ : $6a^2 + 12a = 6a(a + 2)$ .

Q: What is the distributive property?

A: The distributive property is a rule that allows you to expand an expression by multiplying each term in the expression by a factor. For example, in the expression $2(a + b)$ , you can use the distributive property to expand the expression: $2(a + b) = 2a + 2b$ .

Q: How do I use the distributive property to simplify an expression?

A: To use the distributive property to simplify an expression, you need to multiply each term in the expression by a factor. For example, in the expression $2(a + b)$ , you can use the distributive property to simplify the expression: $2(a + b) = 2a + 2b$ .

Q: What are some common mistakes to avoid when simplifying algebraic expressions?

A: Some common mistakes to avoid when simplifying algebraic expressions include:

Not combining like terms when simplifying an expression.
Not factoring out the greatest common factor (GCF) of the terms.
Not using the distributive property to expand expressions and simplify them.
Not simplifying expressions by combining like terms and factoring out the GCF.

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

A: An expression is simplified when there are no like terms that can be combined, and the greatest common factor (GCF) has been factored out. For example, in the expression $2a^2 + 4a$ , the expression is not simplified because the like terms $2a^2$ and $4a$ can be combined: $2a^2 + 4a = 2a(a + 2)$ .

Q: Can you give me some examples of real-world applications of simplifying algebraic expressions?

A: Yes, here are some examples of real-world applications of simplifying algebraic expressions:

In physics, simplifying algebraic expressions is used to describe the motion of objects and the forces acting on them.
In engineering, simplifying algebraic expressions is used to design and optimize systems.
In economics, simplifying algebraic expressions is used to model and analyze economic systems.

Q: How can I practice simplifying algebraic expressions?

A: You can practice simplifying algebraic expressions by working through exercises and problems in a math textbook or online resource. You can also try simplifying expressions on your own and then checking your work with a calculator or by asking a teacher or tutor for help.