Expanding Double Brackets Flashcards

All 6 cards in this deck

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

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 terms: $x^2-4x-45$

How many terms do you get when expanding two binomials, before simplifying?

Four terms.
e.g. $(x+5)(x-9)=x^2-9x+5x-45$

In the expansion of $(x+a)(x+b)$, what are the coefficient of $x$ and the constant term?

Coefficient of $x$ is $a+b$; constant term is $ab$.
e.g. $(x+2)(x+5)=x^2+7x+10$

How do you expand a squared bracket?

e.g. $(2x-5)^2$

Write it as two brackets and expand.
$(2x-5)(2x-5)=4x^2-20x+25$

True or false? $(x+3)^2=x^2+9$.

False. $(x+3)^2=x^2+6x+9$ — the middle terms must be included.

True or false? $(x-2)(x+5)$ and $(x+5)(x-2)$ give the same expansion.

True. Multiplication is commutative, so the order of the two brackets does not change the result.