Question

How do you multiply `(b^2-4b+6)^2`?

Answer 1

See the entire solution process below:

Explanation:

First, we can rewrite this expression as:

`(color(red)(b^2) - color(red)(4b) + color(red)(6))(color(blue)(b^2) - color(blue)(4b) + color(blue)(6))`

To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.

`(color(red)(b^2) xx color(blue)(b^2)) - (color(red)(b^2) xx color(blue)(4b)) + (color(red)(b^2) xx color(blue)(6)) - (color(red)(4b) xx color(blue)(b^2)) + (color(red)(4b) xx color(blue)(4b)) - (color(red)(4b) xx color(blue)(6)) + (color(red)(6) xx color(blue)(b^2)) - (color(red)(6) xx color(blue)(4b)) + (color(red)(6) xx color(blue)(6))`

`b^4 - 4b^3 + 6b^2 - 4b^3 + 16b^2 - 24b + 6b^2 - 24b + 36`

We can now group and combine like terms:

`b^4 - 4b^3 - 4b^3 + 6b^2 + 16b^2 + 6b^2 - 24b - 24b + 36`

`b^4 + (-4 - 4)b^3 + (6 + 16 + 6)b^2 + (-24 - 24)b + 36`

`b^4 - 8b^3 + 28b^2 - 48b + 36`

Answer 2

`color(blue)(b^4-8b^3+28b^2-48b+36`

Explanation:

`color(white)(aaaaaaaaaaaaa)` `b^2-4b+6`
`color(white)(aaaaaaaaaaaaa)` `b^2-4b+6`
`color(white)(aaaaaaaaaaaaa)` `-----`
`color(white)(aaaaaaaaaaaaa)` `b^4-4b^3+6b^2`
`color(white)(aaaaaaaaaaaaaaaa)` `-4b^3+16b^2-24b`
`color(white)(aaaaaaaaaaaaaaaaaaaaaaaa)` `6b^2-24b+36`
`color(white)(aaaaaaaaaaaaa)` `----------`
`color(white)(aaaaaaaaaaaa)` `color(blue)(b^4-8b^3+28b^2-48b+36`