can someone please help me simplify these three expressions if possible
...and if possible please show working out so i can understand better thanks
(a) (x+1)^3 -3x (x+1)
(b) y(2y+3) +2y^2 (y+1)(y-1)
(c) 14x^3 (3-2x) / x^2(x-1)(4x-6)
can someone please help me simplify these three expressions if possible
...and if possible please show working out so i can understand better thanks
(a) (x+1)^3 -3x (x+1)
(b) y(2y+3) +2y^2 (y+1)(y-1)
(c) 14x^3 (3-2x) / x^2(x-1)(4x-6)
$\displaystyle \frac{14x^3(3 - 2x)}{x^2(x - 1)(4x - 6)}$
Note that $\displaystyle 4x - 6 = 2(2x - 3) = -2(3 - 2x)$
So
$\displaystyle \frac{14x^3(3 - 2x)}{x^2(x - 1)(4x - 6)} = -\frac{14x^3(3 - 2x)}{2x^2(x - 1)(3 - 2x)}$
Now we may cancel the common $\displaystyle 3 - 2x$ and the common 2x^2, provided we remember that $\displaystyle x \neq 0, \frac{3}{2}$.
$\displaystyle \frac{14x^3(3 - 2x)}{x^2(x - 1)(4x - 6)} = -\frac{14x^3(3 - 2x)}{2x^2(x - 1)(3 - 2x)} = -\frac{7x}{x - 1};~x \neq 0, \frac{3}{2}$
-Dan