Expanding and simplifying expressions

Multiplying and dividing algebraic terms, expanding brackets with positive and negative terms outside, and expanding then collecting like terms.

Multiplying terms

Multiply the numbers, then the pronumerals: $2x \times 3x = 6x^2$ and $-4ab \times 2a = -8a^2b$. To divide, write as a fraction and cancel: $\dfrac{12x^2y}{4x} = 3xy$.

Expanding

Example 1●●

Expand $-4a(a - 3)$.

$-4a \times a = -4a^2$ and $-4a \times (-3) = +12a$

$-4a^2 + 12a$

Example 2●●

Expand and simplify $3(2x - 5) - 2(x - 4)$.

$6x - 15 - 2x + 8$

$4x - 7$

Flashcards

$2x imes 3x$

$6x^2$

$dfrac{12x^2y}{4x}$

$3xy$

$-(x - 7)$

$-x + 7$

Practice

Expand $-4a(a - 3)$.
Expand and simplify $3(2x - 5) - 2(x - 4)$.
Simplify $2x \times 3x$.
Simplify $\dfrac{12x^2y}{4x}$.
Expand and simplify $4(m + 3) + 3(2m - 5)$.
Expand and simplify $x(x + 5) - 3x$.
Simplify $-4ab \times 2a$.
Expand and simplify $5(y + 3) - 3(y - 1) + 1$.