Expanding Double Brackets Flashcards

All 6 cards in this deck

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 $x^2 + 8x + 16$.