Multiplying out single brackets
To multiply out/expand brackets means multiplying everything inside the bracket by the letter or variable outside the bracket. We call this the Distributive Rule:
$$m(a + b) = ma + mb$$
Example:
$$4(3y+7)=12y+28$$
$$z(z+y−2x)=z^2+zy−2xz$$
Multiplying out double brackets
Two brackets next to each other means the brackets need to be multiplied together. Every term in the first bracket has to be multiplied by every term in the second bracket:
$$(m+n)(a+b)=ma+mb+na+nb$$
Example:
$$(3y+2)(4−y)=$$
$$=3y×4−3y×y+2×4−2×y=$$
$$=12y−3y^2+8−2y=$$
$$=10y−3y^2+8$$
