Question

How do you evaluate `(4f + 1) ( 4f - 1) - 4( 4f + 1)`?

Answer 1

See a solution process below:

Explanation:

First, we can multiply to the two terms on the left using this rule for quadratics:

`(color(red)(x) + color(blue)(y))(color(red)(x) - color(blue)(y)) = color(red)(x)^2 - color(blue)(y)^2`

Let `x = 4f` and `y = 1`

`(color(red)(4f) + color(blue)(1))(color(red)(4f) - color(blue)(1)) - 4(4f + 1) =>`

`color(red)((4f))^2 - color(blue)(1)^2 - 4(4f + 1) =>`

`16f^2 - 1 - 4(4f + 1)`

Next, expand the terms in parenthesis by multiplying each term within the parenthesis by the term outside the parenthesis. Be careful to handle the signs of the individual terms correctly:

`16f^2 - 1 - color(red)(4)(4f + 1) =>`

`16f^2 - 1 - (color(red)(4) xx 4f) - (color(red)(4) xx 1) =>`

`16f^2 - 1 - 16f - 4`

Now, group and combine like terms:

`16f^2 - 16f - 1 - 4 =>`

`16f^2 - 16f - 5`