|
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
|
No comments yet.
Cheatography n. The art of mapping complex subjects into clear, instantly navigable reference guides.
