Simplifying expressions

These laws can be used to simplify algebraic expressions.

Example 6

Simplify each expression by expanding brackets, and then adding and subtracting like terms.

Expression	Simplified expression
\(5x+7x\)	\(12x\)
\(2x-y+3x\)	\(5x-y\)
\(2x-3(y-x)\)	\(2x-3y+3x=5x-3y\)
\(3(2x-5)+5x\)	\(6x-15+5x=11x-15\)
\(7(z+6)-2(3z+4)\)	\(7z+42-6z-8=z+34\)
\(8(q-5)-2(q+3)\)	\(8q-40-2q-6=6q-46\)
\(x(x-5)+x(x+y)\)	\(x^2-5x+x^2+xy=2x^2-5x+xy\)