Evaluate The Following Expressions:1. $35a^2b \times 2ab \div 7ab^2 - 10a^2$2. 11 ( − 7 P ) − 6 ( − 8 P 11(-7p) - 6(-8p 11 ( − 7 P ) − 6 ( − 8 P ]3. 12 A ( 4 A − 6 B ) + 9 B ( 8 A − 4 12a(4a - 6b) + 9b(8a - 4 12 A ( 4 A − 6 B ) + 9 B ( 8 A − 4 ]4. − A ( A + 1 ) − 2 ( 3 − A ) + 4 ( A − 2 -a(a + 1) - 2(3 - A) + 4(a - 2 − A ( A + 1 ) − 2 ( 3 − A ) + 4 ( A − 2 ]5. Y 2 − ( − Y ) 2 Y^2 - (-y)^2 Y 2 − ( − Y ) 2 Find The Solutions For Each

Introduction

Algebraic expressions are a fundamental concept in mathematics, and simplifying them is a crucial skill for students to master. In this article, we will evaluate five different algebraic expressions and find their solutions. We will use the order of operations (PEMDAS) to simplify each expression and find the final answer.

Expression 1: $35a^2b \times 2ab \div 7ab^2 - 10a^2$

To simplify this expression, we need to follow the order of operations (PEMDAS). First, we will multiply the numbers and variables together.

$35a^2b \times 2ab = 70a^3b^2$

Next, we will divide the result by $7ab^2$.

$70a^3b^2 \div 7ab^2 = 10a^2$

Finally, we will subtract $10a^2$ from the result.

$10a^2 - 10a^2 = 0$

The final answer for expression 1 is 0.

Expression 2: $11(-7p) - 6(-8p)$

To simplify this expression, we need to follow the order of operations (PEMDAS). First, we will multiply the numbers and variables together.

$11(-7p) = -77p$

$6(-8p) = -48p$

Next, we will subtract $-48p$ from $-77p$.

$-77p - (-48p) = -77p + 48p = -29p$

The final answer for expression 2 is $-29p$.

Expression 3: $12a(4a - 6b) + 9b(8a - 4)$

To simplify this expression, we need to follow the order of operations (PEMDAS). First, we will multiply the numbers and variables together.

$12a(4a - 6b) = 48a^2 - 72ab$

$9b(8a - 4) = 72ab - 36b$

Next, we will add the two results together.

$48a^2 - 72ab + 72ab - 36b = 48a^2 - 36b$

The final answer for expression 3 is $48a^2 - 36b$.

Expression 4: $-a(a + 1) - 2(3 - a) + 4(a - 2)$

To simplify this expression, we need to follow the order of operations (PEMDAS). First, we will multiply the numbers and variables together.

$-a(a + 1) = -a^2 - a$

$-2(3 - a) = 2a - 6$

$4(a - 2) = 4a - 8$

Next, we will add the three results together.

$-a^2 - a + 2a - 6 + 4a - 8 = -a^2 + 5a - 14$

The final answer for expression 4 is $-a^2 + 5a - 14$.

Expression 5: $y^2 - (-y)^2$

To simplify this expression, we need to follow the order of operations (PEMDAS). First, we will multiply the numbers and variables together.

$-y^2 = -y^2$

Next, we will subtract $-y^2$ from $y^2$.

$y^2 - (-y^2) = y^2 + y^2 = 2y^2$

The final answer for expression 5 is $2y^2$.

Conclusion

In this article, we evaluated five different algebraic expressions and found their solutions. We used the order of operations (PEMDAS) to simplify each expression and find the final answer. By following the order of operations, we can simplify complex algebraic expressions and find the solutions to a variety of problems.

Frequently Asked Questions

• What is the order of operations (PEMDAS)? The order of operations (PEMDAS) is a set of rules that tells us which operations to perform first when simplifying an expression. The acronym PEMDAS stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.
• How do I simplify an algebraic expression? To simplify an algebraic expression, we need to follow the order of operations (PEMDAS). First, we will multiply the numbers and variables together. Next, we will divide the result by any numbers or variables. Finally, we will add or subtract the results.
• What is the difference between a variable and a constant? A variable is a letter or symbol that represents a value that can change. A constant is a number or value that does not change.

References

• "Algebra" by Michael Artin
• "Mathematics for Dummies" by Mary Jane Sterling
• "Algebra and Trigonometry" by James Stewart

Note: The references provided are for general information and are not specific to the content of this article.

Introduction

Algebraic expressions are a fundamental concept in mathematics, and simplifying them is a crucial skill for students to master. In this article, we will answer some frequently asked questions about algebraic expressions and provide examples to help illustrate the concepts.

Q&A

Q: What is the order of operations (PEMDAS)?

A: The order of operations (PEMDAS) is a set of rules that tells us which operations to perform first when simplifying an expression. The acronym PEMDAS stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.

Q: How do I simplify an algebraic expression?

A: To simplify an algebraic expression, we need to follow the order of operations (PEMDAS). First, we will multiply the numbers and variables together. Next, we will divide the result by any numbers or variables. Finally, we will add or subtract the results.

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

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

Q: How do I evaluate an expression with multiple operations?

A: To evaluate an expression with multiple operations, we need to follow the order of operations (PEMDAS). First, we will evaluate any expressions inside parentheses. Next, we will evaluate any exponents. Finally, we will perform any multiplication and division operations from left to right, and then perform any addition and subtraction operations from left to right.

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

A: An equation is a statement that says two expressions are equal. An expression is a group of numbers, variables, and operations that can be evaluated to a single value.

Q: How do I solve an equation with variables on both sides?

A: To solve an equation with variables on both sides, we need to isolate the variable on one side of the equation. We can do this by adding or subtracting the same value to both sides of the equation, or by multiplying or dividing both sides of the equation by the same value.

Q: What is the concept of like terms?

A: Like terms are terms that have the same variable(s) raised to the same power. For example, 2x and 4x are like terms because they both have the variable x raised to the power of 1.

Q: How do I combine like terms?

A: To combine like terms, we need to add or subtract the coefficients of the like terms. For example, if we have the expression 2x + 4x, we can combine the like terms by adding the coefficients: 2x + 4x = 6x.

Examples

Example 1: Simplifying an Expression

Simplify the expression: 2x + 3y - 2x

Solution:

• First, we will combine like terms: 2x - 2x = 0
• Next, we will simplify the expression: 0 + 3y = 3y

The final answer is 3y.

Example 2: Evaluating an Expression

Evaluate the expression: 2(3x + 2) - 5

Solution:

• First, we will evaluate the expression inside the parentheses: 2(3x + 2) = 6x + 4
• Next, we will subtract 5 from the result: 6x + 4 - 5 = 6x - 1

The final answer is 6x - 1.

Example 3: Solving an Equation

Solve the equation: 2x + 3 = 5

Solution:

• First, we will subtract 3 from both sides of the equation: 2x + 3 - 3 = 5 - 3
• Next, we will simplify the equation: 2x = 2
• Finally, we will divide both sides of the equation by 2: 2x/2 = 2/2
• The final answer is x = 1.

Conclusion

In this article, we answered some frequently asked questions about algebraic expressions and provided examples to help illustrate the concepts. We covered topics such as the order of operations, simplifying expressions, evaluating expressions, and solving equations. By following the order of operations and combining like terms, we can simplify complex algebraic expressions and find the solutions to a variety of problems.

Frequently Asked Questions

• What is the order of operations (PEMDAS)?
• How do I simplify an algebraic expression?
• What is the difference between a variable and a constant?
• How do I evaluate an expression with multiple operations?
• What is the difference between an equation and an expression?
• How do I solve an equation with variables on both sides?
• What is the concept of like terms?
• How do I combine like terms?

References

• "Algebra" by Michael Artin
• "Mathematics for Dummies" by Mary Jane Sterling
• "Algebra and Trigonometry" by James Stewart

Note: The references provided are for general information and are not specific to the content of this article.