Coaching Centre
Expanding brackets
Expanding expressions with the distributive law, including negative and pronumeral factors, and expanding then simplifying.
The distributive law
Distributive law
$$a(b + c) = ab + ac \qquad a(b - c) = ab - ac$$Expand $-2x(3x - 5)$.
$-2x \times 3x = -6x^2$ and $-2x \times (-5) = 10x$.
$= -6x^2 + 10x$
Expand and simplify $4(2a + 1) - 3(a - 2)$.
$8a + 4 - 3a + 6$
$= 5a + 10$
$-(x - 4)$
$-x + 4$
$3a(a + 2)$
$3a^2 + 6a$
$-2(5 - y)$
$-10 + 2y$
Expand $-2x(3x - 5)$.
Multiply both terms by $-2x$.
Expand and simplify $4(2a + 1) - 3(a - 2)$.
$8a + 4 - 3a + 6$.
Expand $-(x - 4)$.
Change both signs.
Expand $3a(a + 2)$.
$3a^2 + 6a$.
Expand $-2(5 - y)$.
$-10 + 2y$.
Expand and simplify $2(x + 4) + 5x - 6$.
$2x + 8 + 5x - 6$.
Expand and simplify $x(x + 3) + 4x$.
$x^2 + 3x + 4x$.
Expand and simplify $3(m + 2) - 5(m - 2)$.
$3m + 6 - 5m + 10 = -2m + 16$.
New numbers every time. Keep going until you get five in a row.