Year 10: Simplification and expansion of algebraic expressions

Simplification

Expanding brackets (distribution)

This is the process of multiplying each term inside the brackets by a common factor. For example: $2(x+3)=2x+6$

Combining like terms

Like terms have the same variable raised to the same power. Combine them by adding or subtracting their coefficients. Example: $3x+2x-x=4x$

Examples of simplification

• $3y+5y-2y=6y$
• $4(x+2)=4x+8$
• $2x+3(x-1)=2x+3x-3=5x-3$

Expansion

Expanding brackets (distribution) - reverse of simplification

Multiplying a single term by an expression inside brackets. For example: $2(x+3)=2x+6$

Examples of expansion

• $x(2x+1)=2x^2+x$
• $3(a+b)=3a+3b$
• $-2(x-3)=-2x+6$

Remember to always multiply each term within the brackets!