Expanding Brackets Flashcards

All 11 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: $9p + 13$

When you expand the product of two brackets, how many terms do you get before simplifying?

Four — every term in the first bracket multiplied by every term in the second.
e.g. $(x+2)(x+3) = x^2 + 3x + 2x + 6$

What are the steps to expand and simplify the product of two brackets?

e.g. $(x + 5)(x - 9)$

1. Multiply each term in the first bracket by each term in the second: $x^2 - 9x + 5x - 45$
2. Collect the like $x$ terms: $-9x + 5x = -4x$
3. Write the answer: $x^2 - 4x - 45$

True or false? In $(x + 3)(x + 5)$ the two middle terms of the expansion can be collected into one term.

True.
$5x$ and $3x$ are like terms, giving $8x$.

In the expansion of $(2x + 1)(3x - 2)$, which two terms give the $x^2$ term, and what is it?

The first term of each bracket: $2x \times 3x = 6x^2$.

What does $(x + 4)^2$ mean before you expand it?

$(x + 4)(x + 4)$ — the bracket multiplied by itself.

True or false? $(x + 4)^2 = x^2 + 16$

False.
Expanding $(x+4)(x+4)$ gives $x^2 + 8x + 16$.