Question

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

standard form.
PLEASE HELP

Answer 1

4
`w^(2)` + 2w - 2

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!

Answer 2

4w^2 + 2w

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