What does FOIL stand for, and when can you use it?

First, Outside, Inside, Last. It is the each-term-times-each-term rule carried out in a fixed order. It only applies when both brackets contain exactly two terms.

How do you expand three or more sets of brackets?

Two at a time. Expand and simplify the first pair, then multiply that result by the next bracket, and so on.

International A Level (IAL)MathsEdexcelPure 1FlashcardsAlgebra & FunctionsPolynomials

Polynomials (Edexcel International A Level (IAL) Maths: Pure 1): Flashcards

Exam code: YMA01

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FrontExpanding Brackets
What is the rule for expanding two brackets multiplied together?

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Cards in this collection (6)

What is the rule for expanding two brackets multiplied together?
Every term in one bracket must be multiplied by every term in the other.
So $(a + b) (x + y + z)$ gives six products: $a x + a y + a z + b x + b y + b z$ .
${(a + b)}^{2}$ expands to $a^{2} +______+ b^{2}$ .
${(a + b)}^{2}$ expands to $a^{2} + 2 a b + b^{2}$ .
The middle term comes from the two cross-products, $a b$ and $b a$ , which is exactly what is lost if you square each term separately.
What does FOIL stand for, and when can you use it?
First, Outside, Inside, Last. It is the each-term-times-each-term rule carried out in a fixed order.
It only applies when both brackets contain exactly two terms.
True or False?
${(a + b)}^{3}$ can be expanded by writing the bracket out three times and multiplying.
True.
A cube is simply the bracket multiplied by itself three times, and at that size writing it out is perfectly practical.
How do you expand three or more sets of brackets?
Two at a time.
Expand and simplify the first pair, then multiply that result by the next bracket, and so on.
When is it worth using the binomial expansion instead of writing brackets out?
When the power is large, such as ${(a + b)}^{7}$ .
Writing out and multiplying that many brackets is impractical.

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