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

Dec 2, 2015

$y = 9 {x}^{3} + 24 {x}^{2} - 44 x + 16$

#### Explanation:

The general standard form of a polynomial of degree $4$ is
$\textcolor{w h i t e}{\text{XXX}} y = {a}_{3} {x}^{3} + {a}_{2} {x}^{2} + {a}_{1} {x}^{1} + {a}_{0}$

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

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

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