Question

How do you simplify `(5-2x)^2`?

Answer 1

See a solution process below:

Explanation:

For this special case of quadratics we can use this rule to expand and simplify this expression:

`(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)(5) - color(blue)(2x))^2 =>`

`(color(red)(5) - color(blue)(2x))(color(red)(5) - color(blue)(2x)) =>`

`color(red)(5)^2 - (2 * color(red)(5) * color(blue)(2x)) + color(blue)((2x))^2 =>`

`25 - 20x + 4x^2`

Or, in standard form:

`4x^2 - 20x + 25`