Algebra and functions.

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  • Created by: racheon
  • Created on: 23-02-14 17:00

Simplifying experession by collecting like terms:

a) 3x+2xy=7-x+3xy-9
= 3x-x+2xy+3xy+7-9
= 2x+5xy-2

b) 3x²-6x+4-2x²+3x-3

c) 3(a+b²)-2(3a-4b²)

Simplifying experessions and functions by using rules of indices:

a^m x a^n = a^m+n
a^m ÷ a^n = a^m-n
(a^m)^n = a^mn
a^-m = 1/a^m
a^1/m = m√a
a^n/m = m√a^n

a) x²×x⁵
= x²+⁵
= x⁷

b) 2r²x3r³
= 2x3xr²xr³
= 6r⁵

c) b⁴÷b⁴
=b⁰ = 1

d) 6x^-³÷3x^-⁵

e) (a³)²x2a²

f) (3x²)³÷x⁴

Expaning expressions by multipyling each term inside the bracket by the term outside:

a) 5(2x+3)

b) -3x(7x-4)

c) y²(3-2y³)

d) 4x(3x-2x²+5x³)

e) 2x(5x+3)-5(2x+3)

Factorising expressions:

Factorising is the opposite of expanding expressions.

a) 3x+9

b) x² -5x

c) 8x² +20x

d) 9x² y+15xy²

e) 3x² -9xy

Factorising quadratic expressions:

A quadractic expression has the form ax² +bx+c, where a,b, and c are constants and a doesn't equal 0.
² -y² =(x+y)(x-y) is the difference of 2 squares.

a) 6x² +9x

b) x² -5x-6

c) x² +6x+8

d)6x² -11x-10

e) x² -25
=x² -5²


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