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