Algebraic Expressions Worksheet 1 Answer Key Simplified
The following is a simplified answer key for Algebraic Expressions Worksheet 1. This answer key provides detailed solutions and explanations for each problem.
Section 1: Simplifying Algebraic Expressions
Problem 1: Simplify the expression: 2x + 5 + 3x - 2
📝 Note: Combine like terms to simplify the expression.
Solution: 2x + 5 + 3x - 2 = (2x + 3x) + (5 - 2) = 5x + 3
Problem 2: Simplify the expression: x^2 + 4x - 3x - 2
📝 Note: Combine like terms to simplify the expression.
Solution: x^2 + 4x - 3x - 2 = x^2 + (4x - 3x) - 2 = x^2 + x - 2
Problem 3: Simplify the expression: 3y - 2y + 4y + 1
📝 Note: Combine like terms to simplify the expression.
Solution: 3y - 2y + 4y + 1 = (3y - 2y + 4y) + 1 = 5y + 1
Section 2: Adding and Subtracting Algebraic Expressions
Problem 1: Add the expressions: 2x + 3y and x - 2y
📝 Note: Combine like terms to add the expressions.
Solution: (2x + 3y) + (x - 2y) = 2x + x + 3y - 2y = 3x + y
Problem 2: Subtract the expressions: x^2 - 3x and 2x^2 + 2x
📝 Note: Combine like terms to subtract the expressions.
Solution: (x^2 - 3x) - (2x^2 + 2x) = x^2 - 2x^2 - 3x - 2x = -x^2 - 5x
Problem 3: Add the expressions: 3y + 2z and y - 4z
📝 Note: Combine like terms to add the expressions.
Solution: (3y + 2z) + (y - 4z) = 3y + y + 2z - 4z = 4y - 2z
Section 3: Multiplying Algebraic Expressions
Problem 1: Multiply the expressions: 2x and x + 3
📝 Note: Use the distributive property to multiply the expressions.
Solution: 2x(x + 3) = 2x^2 + 6x
Problem 2: Multiply the expressions: x^2 - 2x and 3x + 1
📝 Note: Use the distributive property to multiply the expressions.
Solution: (x^2 - 2x)(3x + 1) = 3x^3 + x^2 - 6x^2 - 2x = 3x^3 - 5x^2 - 2x
Problem 3: Multiply the expressions: 4y and y - 2
📝 Note: Use the distributive property to multiply the expressions.
Solution: 4y(y - 2) = 4y^2 - 8y
Final Thoughts
In this worksheet, we practiced simplifying, adding, subtracting, and multiplying algebraic expressions. By combining like terms and using the distributive property, we can simplify and manipulate algebraic expressions to solve equations and problems.
What is the importance of simplifying algebraic expressions?
+Simplifying algebraic expressions is important because it allows us to combine like terms, eliminate unnecessary variables, and make the expression more manageable. This can help us solve equations and problems more efficiently.
How do I combine like terms in algebraic expressions?
+To combine like terms in algebraic expressions, look for terms that have the same variable(s) raised to the same power. Then, add or subtract the coefficients of those terms.
What is the distributive property in algebra?
+The distributive property in algebra states that for any real numbers a, b, and c, a(b + c) = ab + ac. This property allows us to multiply a single term by a binomial or polynomial expression.
