Expanding brackets

Using the distributive law to expand brackets, including negative terms outside the bracket, and simplifying the result.

The distributive law

Distributive law

$$a(b + c) = ab + ac$$

Multiply the term outside by every term inside.

Two expressions, one graph

The bracket form and the expanded form draw exactly the same line, so they are equivalent.

Example 1●

Expand $4(2x - 3)$.

$4 \times 2x - 4 \times 3 = 8x - 12$

Example 2: negative outside●●

Expand $-3(a - 5)$.

$-3 \times a = -3a$ and $-3 \times (-5) = +15$

$= -3a + 15$

Example 3●●

Expand and simplify $2(x + 4) + 3(x - 1)$.

$2x + 8 + 3x - 3$

$= 5x + 5$

Flashcards

$a(b + c)$

$ab + ac$

$-2(x - 4)$

$-2x + 8$

$x(x + 3)$

$x^2 + 3x$

Practice