Question

What is the standard form of a polynomial `(2x – 6)^2`?

Answer 1

See a solution process below:

Explanation:

We can use this special rule for quadratics to put this expression in standard form.

`(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`

Substituting the values from the problem gives:

`(color(red)(2x) - color(blue)(6))^2 => (color(red)(2x) - color(blue)(6))(color(red)(2x) - color(blue)(6)) => (color(red)(2x))^2 - (2 * color(red)(2x) * color(blue)(6)) + color(blue)(6)^2 =>`

`4x^2 - 24x + 36`