Question

How do you write `y=3(x-5)(x+2)` in standard form?

Answer 1

`y=3x^2-9x-30`

Explanation:

`color(blue)((x-5))color(green)((x+2))=`

`{: (underline(xx),underline(" | "),underline(color(blue)x),underline(color(blue)(-5))), (color(green)x," | ",x^2,-5x), (underline(color(green)(+2)),underline(" | "),underline(+2x),underline(-10)), (,color(red)(x^2),color(red)(-3x),color(red)(-10)) :}`

Therefore
`color(white)("XXX")3(x-5)(x+2)=3(color(red)(x^2-3x-10))`

`color(white)("XXXXXXXXXXXX")=3x^2-9x-30`

Note that to be in "standard form" the polynomial must be arranged with the terms in descending degree order (which this already is).