2m x 4n
6ab
6 x ab
y6y64hthtr
X2
3a x 2b
2 x 2 x 3 x 3
x^2-x-6
y = 1/2 x - 3/2
2 x 2 x 2 x 3 x 3 = 72 2^3 x 3^2 = 72
√3 x 2√3 = 2 (√3)2 = 2 x 3 = 6
Factor them. 2 x 2 x b x b = 4b2 2 x 3 x b x b x b = 6b3 Combine the factors, eliminating duplicates. 2 x 2 x 3 x b x b x b = 12b3, the LCM
2b
-1
(ax + b)^3 = a^3*x^3 + 3*a^2*x^2*b + 3*a*x*b^2 + b^3. Sorry, but it is so clumsy doing this without superscripts!
Explanation: The difference of squares identity can be written: a 2 − b 2 = ( a − b ) ( a b ) The difference of cubes identity can be written: a 3 − b 3 = ( a − b ) ( a 2 a b b 2 ) The sum of cubes identity can be written: a 3 b 3 = ( a b ) ( a 2 − a b b 2 ) So: x 6 − y 6 = ( x 3 ) 2 − ( y 3 ) 2 = ( x 3 − y 3 ) ( x 3 y 3 ) = ( x − y ) ( x 2 x y y 2 ) ( x y ) ( x 2 − x y y 2 ) If we allow Complex coefficients, then this reduces into linear factors: = ( x − y ) ( x − ω y ) ( x − ω 2 y ) ( x y ) ( x ω y ) ( x ω 2 y ) where ω = − 1 2 √ 3 2 i = cos ( 2 π 3 ) sin ( 2 π 3 ) i is the primitive Complex cube root of 1 .
b represents a number ^ represents raised to a power (x - b)(x^2+ bx +b^2) For example: (X^3 - 27) (x - 3)(x^2 + 3x + 3^2) = (x - 3)(x^2 + 3x + 9)
5