Algebra I

Variable (definition)

A letter that represents a number. Its value can change e.g. 2x

Coefficient (definition)

The number in front of the variable

Constant (definition)

A number that stays the same (a number with no variable) e.g. 2

Algebraic expression (definition)

When we put an operation e.g. + between two terms

Polynomial (definition)

An algebraic equation where all the variables are raised to non-negative whole numbers

degree (definition)

The highest power that x is raised to.

If we’re multiplying two of the same variable what do we do with the powers?

Add the powers

If there is no constant or variable raised to a specific power, what would you write down?

0

Method for squaring brackets (3)

Square first term. Multiply and double. Square the last

Factorising (definition)

Reverse of expanding

Formula for difference/sum of two cubes (+)

a3 +b3 = (a+b) (a2 +ab + b2)

Formula for difference/sum of two cubes (-)

a3 - b3 = (a-b) (a2 + ab + b2)

What method should you use to divide fractions with?

TUAM

What does TUAM stand for?

Turn Upside down And Multiply

Binomial Expansion (Definition)

Where an expression of 2 terms is multiplied by itself a number of times

Binomial Theorem (Formula)

(x+y)ⁿ = (nC0) xⁿ + (nC1) x^n-1y … (nCn) yⁿ

Formula for nth term

∑ (nCr) x^n-r y^r (pg 20)

What do you do when finding out what r is in the formula for nth term?

Start the counting at zero e.g. 4th term ∴ r=3