Year 10: Simplification and expansion of algebraic expressions

Simplification

Simplifying an algebraic expression means rewriting it in its simplest form. This is usually done by combining like terms.

• Like Terms: Terms with the same variables and powers. Example: 2x + 3x = 5x
• Combining Like Terms: Add or subtract the coefficients of like terms.
• Example: 3x² + 2x - x² + 5x = (3x² - x²) + (2x + 5x) = 2x² + 7x

Expansion (Brackets)

Expansion means multiplying out brackets. Remember the distributive property: a(b + c) = ab + ac

• The Product of a Single Term and a Binomial: a(b + c) = ab + ac
• The Product of Two Binomials: (a + b)(c + d) = ac + ad + bc + bd
• Example: 2(x + 3) = 2x + 6
• Example: (x + 2)(x + 3) = x² + 3x + 2x + 6 = x² + 5x + 6

Practice is key! Work through plenty of examples to become comfortable with these concepts.