Question

What is the standard form of `y= (x-6)(x-4)(x-1)`?

Answer 1

`y=x^3-11x^2+34x-24`

Explanation:

To rewrite the equation in standard form, start by expanding the first two brackets:

`y=(color(red)x` `color(green)(-6))(color(orange)x` `color(blue)(-4))(x-1)`

`y=(color(red)x(color(orange)x)` `color(red)(+x)(color(blue)(-4))` `color(orange)(+x)(color(green)(-6))` `color(green)(-6)(color(blue)(-4)))(x-1)`

Simplify.

`y=(x^2-4x-6x+24)(x-1)`

`y=(x^2-10x+24)(x-1)`

Expand the remaining two brackets:

`y=(color(red)(x^2)` `color(orange)(-10x)` `color(blue)(+24))(color(green)x` `color(purple)(-1))`

`y=color(red)(x^2)(color(green)x)` `color(red)(+x^2)(color(purple)(-1))` `color(orange)(-10x)(color(green)x)` `color(orange)(-10x)(color(purple)(-1))` `color(blue)(+24)(color(green)x)` `color(blue)(+24)(color(purple)(-1))`

Simplify.

`y=x^3-x^2-10x^2+10x+24x-24`

`y=x^3-11x^2+34x-24`