Expanding & Simplifying Single Brackets Flashcards

All 5 cards in this deck

What does it mean to expand a bracket?

e.g. expand $2(a + d)$

Multiply every term inside the bracket by the term outside.
$2(a+d) = 2a + 2d$

True or false? $3(4 - 2x) = 12 - 2x$

False.
Both terms must be multiplied by $3$: $12 - 6x$.

What are the steps to expand a bracket with an algebraic term outside?

e.g. expand $x(x - 4)$

1. Multiply the outside term by the first term: $x \times x = x^2$
2. Multiply the outside term by the second term, keeping its sign: $x \times (-4) = -4x$
3. Write the terms together: $x^2 - 4x$

When a bracket has a negative number in front, what do you multiply each term inside by?

e.g. $-2(1 - 2x)$

By the whole negative number, including its sign.
$-2(1 - 2x) = -2 + 4x$

What are the steps to expand and simplify two single brackets?

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

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