Question

2(x-2)+x(2-x)

Answer 1

hint: \(\large (b-a) = -(a-b)\)

Answer 2

what formula is that?

Answer 3

it's not really a formula...it's a way of manipulation see.. if you distribute \(-(a-b) = -a + b = b-a\)

see?

Answer 4

??

Answer 5

i distributed the negative signs... \(-(a-b) = -(a) - (-b) = -a + b = b -a \quad \text{(according to commutative property)}\)

Answer 6

what formula is -(a-b)??

Answer 7

it is not a formula...i factored out -1 from (b-a)

Answer 8

do you get it?

Answer 9

not really

Answer 10

hmm how should i explain this...like i said i factored out -1...let's go with that explanation...in factoring you divide each factor by the value your factoring right? for example when you factor out x from 2x^2 + x it's \(\large x(\frac{2x^\cancel{2}}{\cancel{x}} + \frac{\cancel{x}}{\cancel{x}}) = x(2x +1)\) do you agree with me on that one?

Answer 11

yea

Answer 12

so if i factor out -1 from (b-a)

\(-1(\frac{b}{-1}) - \frac{a}{-1} = -1[-b - (-a) ]= -1(-b + a)\)

agree?

Answer 13

yea

Answer 14

and -b + a according to commutative property is also a - b right?

Answer 15

but where did (b-a) come from

Answer 16

is that a formula

Answer 17

it was an example :)

Answer 18

ok

Answer 19

and for simplicity sake yeah let's say it's a formula \((b-a) = -(a-b)\)

so can you solve your problem now?

Answer 20

yes