Question

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

Answer 1

`y=9x^3+24x^2-44x+16`

Explanation:

The general standard form of a polynomial of degree `4` is
`color(white)("XXX")y=a_3x^3+a_2x^2+a_1x^1+a_0`

Converting `y=(x+4)(3x-2)^2`
is simply a matter of multiplying the factors on the right side of this equation.

In case multiplication is the actual problem:
`(3x-2)^2:`
`color(white)("XXX"){: (xx,"|",3x,-2), ("---",,"----","----"), (3x,"|",9x^2,-6x), (-2,"|",-6x,+4), ("---",,"----","----"), (=,9x^2,-12x,+4) :}`

`(x+4)(3x-2)^2:`
`color(white)("XXX"){: (xx,"|",9x^2,-12x,+4), ("---",,"----","----","----"), (x,"|",9x^3,12x^2,+4x), (+4,"|",36x^2,-48x,+16), ("---",,"----","----","----"), (=,9x^3,+24x^2,-44x,+16) :}`