Question

If B = 2w2 + 1 and C = 1 – W, find an expression that equals 2B – 2C in

Answer 1

Answer:

4$w^{2}$ + 2w - 2

Step-by-step explanation:

Write what you know.

B = 2$w^{2}$

C = 1 - w

We have to create an equation where 2B - 2C

We plug in what was given for B and C.

B = 2$w^{2}$        C = 1 - w

2*( 2$w^{2}$ ) - 2*( 1 - w)     Multiply it out

4$w^{2}$ - 2 * 1 - 2 * - w

4$w^{2}$ - 2 - (-2w)

4$w^{2}$ - 2 + 2w   re-write

4$w^{2}$ + 2w - 2

For fun let's factor it!

4$w^{2}$ + 2w - 2  

Let's pull out 2 because we can see it's common in all the terms.

2(2$w^{2}$ + w - 1)

Now we concentrate on the second part.

(2$w^{2}$ + 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$w^{2}$ + 2w - w - 1

2$w^{2}$ + w - 1   Don't forget our 2 in front!

2 ( 2$w^{2}$ + w - 1 )

2 * 2$w^{2}$ + 2 * w - 2 * 1

4$w^{2}$ + 2w - 2   Which is what we started with! We guessed right!