# Algebra and functions.

- 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

=3x²-2x²-6x+3x+4-3

=x²-3x+1

c) 3(a+b²)-2(3a-4b²)

=3a+3b²-6a+8b²

=-3a+11b²

**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

=b⁴-⁴

=b⁰ = 1

d) 6x^-³÷3x^-⁵

=6÷3×x^-³÷x^-5

=2×x²

=2x²

e) (a³)²x2a²

=a⁶x2a²

=2xa⁶+²

=2a⁸

f) (3x²)³÷x⁴

=27x⁶÷x⁴

=27÷1×x⁶÷x⁴

=27×x⁶-⁴

=27x²

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

a) 5(2x+3)

=10x+15

b) -3x(7x-4)

=-21x²+12x

c) y²(3-2y³)

=3y²-2y⁵

d) 4x(3x-2x²+5x³)

=12x²-8x³+20x⁴

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

=10x²+6x-10x-16

=10x²-4x-15

**Factorising expressions:**

*Factorising is the opposite of expanding expressions.*

a) 3x+9

=3(x+3)

b) x² -5x

=x(x-5)

c) 8x² +20x

=4x(2x+5)

d) 9x² y+15xy²

=3xy(3x+5y)

e) 3x² -9xy

=3x(x-3y)

**Factorising quadratic expressions:**

*A quadractic expression has the form ax*² *+bx+c, where a,b, and c are constants and a doesn't equal 0.
x*²

*-y*²

*=(x+y)(x-y) is the difference of 2 squares.*

a) 6x² +9x

=3x(2x+3)

b) x² -5x-6

=(x-6)(x+1)

c) x² +6x+8

=(x+2)(x+4)

d)6x² -11x-10

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

e) x² -25

=x² -5²

=(x+5)(x-5)

…

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