Expanding & Simplifying Single Brackets Flashcards

All 6 cards in this deck

What does it mean to expand a single bracket?

e.g. $3(x+4)$

Multiply every term inside the bracket by the term outside.
$3(x+4)=3x+12$

True or false? $4(x+3)$ expands to $4x+3$.

False. The $4$ multiplies both terms: $4x+12$.

How do you expand a bracket when the term outside contains a variable?

e.g. $4p(p^2+3p)$

Multiply each term inside by the whole term outside, adding the indices.
$4p(p^2+3p)=4p^3+12p^2$

What are the steps to expand and simplify two single brackets with a subtraction in front of the second?

e.g. $5(p+3)-2(1-2p)$

1. Expand the first bracket: $5p+15$
2. Multiply the second bracket by $-2$ throughout: $-2+4p$
3. Collect like terms: $9p+13$

True or false? $-2(1-2p)$ expands to $-2-4p$.

False. It is $-2+4p$, because $-2\times-2p=+4p$.

What happens to the terms when a bracket is subtracted?

e.g. $-(x^2-2x-4)$

Every term inside changes sign.
$-(x^2-2x-4)=-x^2+2x+4$