Solve y=3(h-3)^3-7(h-3)

$$y = 3 ( h - 3 ) ^ { 3 } - 7 ( h - 3 )$$

Solve for y

$$y=\left(h-3\right)\left(3\left(h-3\right)^{2}-7\right)$$

Solution Steps

Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(h-3\right)^{3}.

$$y=3\left(h^{3}-9h^{2}+27h-27\right)-7\left(h-3\right)$$

Use the distributive property to multiply 3 by h^{3}-9h^{2}+27h-27.

$$y=3h^{3}-27h^{2}+81h-81-7\left(h-3\right)$$

Use the distributive property to multiply -7 by h-3.

$$y=3h^{3}-27h^{2}+81h-81-7h+21$$

Combine 81h and -7h to get 74h.

$$y=3h^{3}-27h^{2}+74h-81+21$$

Add -81 and 21 to get -60.

$$y=3h^{3}-27h^{2}+74h-60$$