Algebra Homework: Simplifying and Solving Equations

This page presents a comprehensive simplifying challenging algebra equations step by step worksheet with a variety of questions designed to reinforce key algebraic concepts. The worksheet covers multiple topics, providing students with ample practice in simplifying algebraic expressions, expanding brackets, and solving equations.

Highlight: The worksheet includes a diverse range of question types, from basic simplification to more complex operations involving exponents and fractions.

1. Simplifying Expressions: The first question focuses on simplifying algebraic expressions by combining like terms. For example, "7a + 7b + 5a - b" is simplified to "12a + 6b".

Example: In the expression "4d + 7d - 3d", like terms are combined to yield "8d".

2. Simplifying with Negative Terms: Some questions involve simplifying expressions with negative terms, such as "29s - 5s + 2s - 3s", which simplifies to "23s".

3. Multiplying Algebraic Expressions: The worksheet includes problems on multiplying algebraic expressions with variables and exponents. For instance, "13x²y⁴ × 20x³y = 260x⁵y⁵".

Vocabulary: Exponents are used to indicate repeated multiplication of the same factor. In "x²", the 2 is the exponent, meaning x is multiplied by itself twice.

4. Simplifying Fractions: There are questions on simplifying algebraic fractions, such as "46² ÷ 6² = 6³".

5. Expanding and Simplifying: Students are asked to expand expressions and then simplify them, like in the question "(3x + 2)(4x - 3)".

6. Equivalent Expressions: The worksheet includes a section on identifying equivalent expressions, reinforcing the concept that different-looking expressions can represent the same mathematical relationship.

Definition: Equivalent expressions are algebraic expressions that simplify to the same result, despite looking different initially.

7. Solving Equations: The final questions involve solving equations and finding values for variables, such as "4x = 3y - 2" and "20² + 5b² - a = 6, b = 2".

This comprehensive worksheet provides excellent practice for students working on simplifying challenging algebra equations step by step with answers, making it an invaluable resource for GCSE preparation and general algebra skill development.