Solve y=2(-4(x-1))^3+3

$$y = 2 ( - 4 ( x - 1 ) ) ^ { 3 } + 3$$

Solve for y

$$y=-128\left(x-1\right)^{3}+3$$

Solution Steps

Use the distributive property to multiply -4 by x-1.

$$y=2\left(-4x+4\right)^{3}+3$$

Use binomial theorem \left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} to expand \left(-4x+4\right)^{3}.

$$y=2\left(-64x^{3}+192x^{2}-192x+64\right)+3$$

Use the distributive property to multiply 2 by -64x^{3}+192x^{2}-192x+64.

$$y=-128x^{3}+384x^{2}-384x+128+3$$

Add 128 and 3 to get 131.

$$y=-128x^{3}+384x^{2}-384x+131$$

Solve for x

$$x=-\frac{2^{\frac{2}{3}}\sqrt[3]{y-3}}{8}+1$$