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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: $2 x + 3 x = 5 x$
Combining like terms: Add or subtract the coefficients of like terms.
Example: $3 x^{2} + 2 x - x^{2} + 5 x = (3 x^{2} - x^{2}) + (2 x + 5 x) = 2 x^{2} + 7 x$

Expansion (Brackets)

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

The Product of a Single Term and a Binomial: $a (b + c) = a b + a c$
The Product of Two Binomials: $(a + b) (c + d) = a c + a d + b c + b d$
Example: $2 (x + 3) = 2 x + 6$
Example: $(x + 2) (x + 3) = x^{2} + 3 x + 2 x + 6 = x^{2} + 5 x + 6$