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

  • Thread starter LizzzyBF
  • Start date
  • #1
6
0

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.
 

Answers and Replies

  • #2
99
0
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!
 
  • #3
6
0
Thank you so much! :smile:
 

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