Answer:
4[tex]w^{2}[/tex] + 2w - 2
Step-by-step explanation:
Write what you know.
B = 2[tex]w^{2}[/tex]
C = 1 - w
We have to create an equation where 2B - 2C
We plug in what was given for B and C.
B = 2[tex]w^{2}[/tex] C = 1 - w
2*( 2[tex]w^{2}[/tex] ) - 2*( 1 - w) Multiply it out
4[tex]w^{2}[/tex] - 2 * 1 - 2 * - w
4[tex]w^{2}[/tex] - 2 - (-2w)
4[tex]w^{2}[/tex] - 2 + 2w re-write
4[tex]w^{2}[/tex] + 2w - 2
For fun let's factor it!
4[tex]w^{2}[/tex] + 2w - 2
Let's pull out 2 because we can see it's common in all the terms.
2(2[tex]w^{2}[/tex] + w - 1)
Now we concentrate on the second part.
(2[tex]w^{2}[/tex] + w - 1) We will have 2 factors.
( ) ( ) We know w will be in each
( w ) ( w ) We also know one of them will have a 2 in front of the w.
( 2w ) ( w ) Now let's fill in the sign, we know one will be + and the other will be - because the last term is negative and a + * + = + and - * - = +
We don't know which goes where yet, so let's guess.
( 2w - ) ( w + ) Now we need to think of all the ways we can multiply to get 1, because 1 is the last term (actually - 1). We are lucky because there is only one option, and that's 1 x 1!
( 2w - 1 ) ( w + 1 )
( 2w - 1 ) ( w + 1 ) Let's check our answer and multiply it out.
2w * w + 2w * 1 - 1 * w - 1 * 1
2[tex]w^{2}[/tex] + 2w - w - 1
2[tex]w^{2}[/tex] + w - 1 Don't forget our 2 in front!
2 ( 2[tex]w^{2}[/tex] + w - 1 )
2 * 2[tex]w^{2}[/tex] + 2 * w - 2 * 1
4[tex]w^{2}[/tex] + 2w - 2 Which is what we started with! We guessed right!
