Question

How do you simplify `3x ( 2x + 3) - 4( x ^ { 2} - 2x)`?

Answer 1

`2x^2+17x`

Explanation:

1) First, multiply the bracket(s) out, this gets us:

`color(red)(3x(2x+3)`

=> `3x xx 2x=6x^2`

=> `3x xx 3=9x`

`color(red)(-4(x^2-2x)`

=> `-4 xx x^2=-4x^2`

=> `-4 xx -2x=8x`

Since `color(red)(-1 xx -1=1`

`therefore` `color(Red)(-4 xx -2x=8x`

2) Plug this back into the expression, replacing the brackets before with the answers we just got gets us:

`color(green)(6x^2)+color(blue)(9x)color(GREEN)(-4x^2)color(BLUE)(+8x)`

3) Collect like-terms to simplify this further:

`color(green)(6x^2-4x^2=2x^2`

`color(Blue)(9x+8x=17x`

4) Then plug this back into the expression, as it is fully simplified. Leaving us with:

`color(red)(2x^2+17x`

Answer 2

`2x^2+17x`

Explanation:

`"distribute brackets and collect like terms"`

`=color(red)(6x^2)color(blue)(+9x)color(red)(-4x^2)color(blue)(+8x)`

`=2x^2+17x`