Solve y=4(3x-5)^3*3-x

$$y = 4 ( 3 x - 5 ) ^ { 3 } \cdot 3 - x$$

Solve for y

$$y=-\left(-12\left(3x-5\right)^{3}+x\right)$$

Solution Steps

Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(3x-5\right)^{3}.

$$y=4\left(27x^{3}-135x^{2}+225x-125\right)\times 3-x$$

Multiply 4 and 3 to get 12.

$$y=12\left(27x^{3}-135x^{2}+225x-125\right)-x$$

Use the distributive property to multiply 12 by 27x^{3}-135x^{2}+225x-125.

$$y=324x^{3}-1620x^{2}+2700x-1500-x$$

Combine 2700x and -x to get 2699x.

$$y=324x^{3}-1620x^{2}+2699x-1500$$