Question

How do you multiply `(2ab+c^2)^2`?

Answer 1

See a solution process below:

Explanation:

This is a special form of the quadratic equation:

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

Let `color(red)(x)` equal `2ab`

Let `color(blue)(y)` equal `c^2`

Substituting gives:

`(color(red)(2ab) + color(blue)(c^2))^2 =>`

`(color(red)(2ab) + color(blue)(c^2))(color(red)(2ab) + color(blue)(c^2)) =>`

`color(red)((2ab))^2 + (2 xx color(red)(2ab) xx color(blue)(c^2)) + color(blue)((c^2))^2 =>`

`4a^2b^2 + 4abc^2 + c^4`