Expanding and Simplifying Two Sets of Double Brackets (most likely really easy)

[LizzzyBF]

Homework Statement

Expand and Simplify 6(x-1)(x+2)-(1-x)(2+x)

Homework Equations

The answer in the book is 7x^2+7x-14

The Attempt at a Solution

I've tried several ways, but all of them give the wrong answer.
I'm not sure what to do with the negative in the middle. I know it makes everything in the bracket the opposite sign (i.e. - becomes +, + becomes -) but is that for both (1-x) AND (2+x), or just (1-x)?
I'm also not sure whether to multiply the (x+2) by 6 as well as the (1-x).

first I expanded to get 6x-6+x^2-x+2x-2-2-x+2x_x^2, which simplified to 2x^2+14x+4
then I tried expanding again, without multiplying the (x+2) by 6, and got 6x-6+x^2-x+2x-2-2-x+2x+x^2 = 2x^2+6x+2

I know this is really easy, it's my first piece of maths homework for the year, but I've spent two hours trying different ways to do this problem.

 

[1/2"]

Try this,
6(x-1)(x+2)-(1-x)(2+x)

=6(x-1)(x+2)+(-1)(1-x)(2+x)[-(1-x)(2+x) means (-1)(1-x)(2+x)]

= 6(x-1)(x+2)+(x-1)(2+x)[here i multiply -1 to (x-1) only ]

let (x-1)(x+2) be a [ just for simplicity]
then we have,

=6a+a

=7a
now a=(x-1)(x+2) =(x²+ 2x -1x -2)= (x²+1x-2)

=7(x²+1x-2)
=7x²+7x-14

I hope it helps!

 

[LizzzyBF]

Thank you so much!