Expanding Triple Brackets Flashcards

All 5 cards in this deck

What are the steps to expand and simplify three binomials?

e.g. $(x+1)(x+2)(x+3)$

1. Multiply two of the brackets: $(x+1)(x+2)=x^2+3x+2$
2. Multiply that quadratic by the remaining bracket, each term by each: $x^3+3x^2+2x+3x^2+9x+6$
3. Collect like terms: $x^3+6x^2+11x+6$

What form does the expansion of three linear brackets take?

A cubic, $ax^3+bx^2+cx+d$.

How many terms do you get when multiplying a simplified 3-term quadratic by a binomial, before simplifying?

Six terms.

True or false? When expanding three brackets you must multiply the first two brackets first.

False. Any pair can be multiplied first; the final cubic is the same.

When three linear brackets are expanded to $ax^3+bx^2+cx+d$, how can you check $a$ and $d$ quickly?

e.g. $(2x+1)(x+3)(3x+7)$

$a$ is the product of the $x$-coefficients and $d$ is the product of the constants.
$a=2\times1\times3=6$, $d=1\times3\times7=21$