Question

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

Answer 1

`y=-x^3+2x^2-16x+8`

Explanation:

The standard form of a general equation of degree `3` is
`color(white)("XXX")y=ax^3+bx^2+cx+d`

To convert the given equation: `y=color(red)((4x)(x-3))-color(blue)((x^2-4)(-x+2))`
into standard form, we must first expand the expression on the right side:

`y=color(red)((4x^2-12x)) - color(blue)((x^3+2x^2+4x-8))`

`color(white)("XX")= color(blue)(-x^3)+color(red)(4x^2)-color(blue)(2x^2)color(red)(-12x)-color(blue)(4x)color(blue)(+8)`

`color(white)("XX")=-x^3+2x^2-16x+8`
(which is in standard form)