Year 7: Simplification and Expansion of Algebraic Expressions (Advanced)

Advanced Simplification Techniques

In advanced expressions, be systematic about grouping like terms.

Example with mixed terms:

5x² - 3x + 2 - 2x² + 4x - 7

1. Group by power: (5x² - 2x²) + (-3x + 4x) + (2 - 7)
2. Combine: 3x² + x - 5

Expanding Complex Expressions

With multiple variables and powers, expand methodically:

• 2x(3x + 4y - 5) = 6x² + 8xy - 10x (multiply 2x by each term)
• -3(2a² - ab + 1) = -6a² + 3ab - 3 (distribute negative)
• a(a + b + c) = a² + ab + ac (variable multiplication)

Combining Expansion and Simplification

Multi-step problems often require both skills:

Example: 2(3x + 2) + 4(x - 1)

1. Expand first: 6x + 4 + 4x - 4
2. Simplify: 10x

Introduction to Factoring

Factoring is the reverse of expanding. Find the common factor:

• 2x + 4 = 2(x + 2) (common factor is 2)
• 3ab + 6a = 3a(b + 2) (common factor is 3a)
• x² + 3x = x(x + 3) (common factor is x)