y=(x-5)(x-2) +(3x-1)²
The standard form of a polynomial is :
y=sum_(k=0)^(n)a_kx^k=a_0+a_1x+...+a_nx^n, where a_k in RR and k in NN.
In order to write it, you need to develop each term,
and to sum each term of same degree.
y=(color(red)x-color(blue)5)(x-2)+(color(green)(3x)-color(purple)1)*(3x-1)
y=color(red)(x(x-2))-color(blue)(5(x-2))+color(green)(3x(3x-1))-color(purple)((3x-1))
y=color(red)(x*x-2*x)+(color(blue)(-5*x-5*(-2)))+color(green)(3x*3x-3x*1)-color(purple)((3x-1))
y=color(red)(x²-2x)-color(blue)(5x+10)+color(green)(9x²-3x)-color(purple)(3x+1)
Finally, let's sum each term of same degree :
y=(color(red)(1)color(green)(+9))^(color(orange)(=10))x²+(color(red)(-2)color(blue)(-5)color(green)(-3)color(purple)(-3))^(color(orange)(=-13))x(color(blue)(+10)color(purple)(+1))^(color(orange)(=11))
y=10x²-13x+11
\0/ Here's our answer !
