Question

What is `(x-3)(x-1)-(3x+4)(2x-3)`?

Answer 1

`-5x^2-3x+15`

Explanation:

I am going to use squarer brackets just to group things more obviously. Their shape has no significance other than that!

`"Given: "color(brown)(color(blue)((x-3))(x-1)" "-" "color(green)((3x+4))(2x-3)`

Write as:

`[color(white)(.)color(brown)(color(blue)(x)(x-1) color(blue)(-3)(x-1) )" ] " -" "[color(white)(.)color(brown)(color(green)(3x)(2x-3)color(green)(+4)(2x-3)color(white)(.))]`

`[x^2-x-3x+3 ]" "-" "[6x^2-9x+8x-12]`

As there is a minus sign outside the right hand side bracket multiply everything inside by `-1`

`color(brown)("I have left the LHS bracket in place to make clearer what is happening")`

`[x^2-x-3x+3] -6x^2+9x-8x+12`

`x^2-x-3x+3-6x^2+9x-8x+12`

Collecting like terms

`x^2-6x^2-x-3x+9x-8x+3+12`

`-5x^2-3x+15`