Question

What is the standard form of `y-4(x-2)^3= -(x-1)^2+3x`?

Answer 1

standard form:
`color(white)("XXX")y="polynomial in "x`
where the terms of `"polynomial in " x` are arranged in descending degree.

Explanation:

Given
`color(white)("XXX")y-4(x-2)^3=-(x-1)^2+3x`

Expand the expressions:
`color(white)("XXX")y-4(x^3-6x^2+12x-8)=-(x^2-2x+1)+3x`

`color(white)("XXX")y-(4x^3-24x^2+48x-32)= -x^2+5x-1`

Shift the sub-expression in `x` to the right side:
`color(white)("XXX")y=4x^3-24x^2+48x-32-x^2+5x-1`

Simplify and ensure the terms are in descending degree:
`color(white)("XXX")y=4x^3-25x^2+53x-33`