Quadratic Expressions & Trigonometry Cheat Sheet by NiffyYT

5x²+10x	LCM is 5x
= 5x(x+2)

Rewrite as a difference of two squares	x²-16
= x²-4²	= (x+4)(x-4)
Rewrite as a difference of two squares
16x²-9y²	= (4x)²-­(3y)²
= (4x+3y­)(4­x-3y)
Difference of squares in the form ab²x²-­ac²y²
18x²y⁴­-98x2z2	= 2x2(9y­⁴-49z2)
= 2x²[(3­y²)­²-(­7z)²]	= 2x²(3y­+7z­)(3­y-7z)

Factorise x² +4x+3	Find factors of 3, summing to 4
1 & 3	= (x+1)(x+3)
Factorise x²-12x+32	Find factors of 32, summing to -12
-4 & -8	= (x-4)(x-8)

Is 16x²-8²+1 a perfect square?	a=4, b=1
-2x4x1=8	Yes, (4x-1)²

5x+10/5	5(x+2/5
= (x+2)
Factorise where possible
x²-5x+­6/x­²-7x+12	= (x-3)(­x-2­)/(­x-3­)(x-4)
= (x-2)(x-4)
Multiply & Dividing	2x²/x²+x ÷ 4x²/6x+6
= 2x²/x(x+1) ÷ 4x²/6(x+1)	= 2x²/x(x+1) X 6(x+1)/4x²
=6/2x = 3/x
Adding & Subtra­cting
5/xy + 6/xy - m/xy	5+6-m/xy
= 11-m/xy
b. when the denomi­nators are different	1/x - 2/y
LCD = xy	1 X y/xy - 2 X x/xy
1/x - 2/y = y/xy - 2x/xy = y-2x/xy

c² = a² + b²	SOH CAH TOA
DMS button on calculator	XX*XX'XX''
Find the missing side. x
tan77* = x/5.9	x = 5.9tan77*
= 26
b. x in denomi­nator
tan29*­16'­=23.1/x	x = 23.1/t­an2­9*16'
= 41.22
Find a missing angle
use sin⁻¹ tan⁻¹ or cos⁻¹ with existing sides

Substi­tution Method
y = 3x-7 (1)	2x-3y=12 (2)
Sub (1) into (2)	2x+3(3x+7) = 12
2x+9x-­21=12	11x = 33
x = 3
Elimin­ation Method
3x-2y =14 (1)
5x+2y = 18 (2)	+
------­---­---­---­---­---­---­-----
8x = 32	x = 4
sub into (2)
20+2y=18	2y = -2
-20 both sides	y = -1