Question

How do you simplify `(6x y + 8) ^ { 2}`?

Answer 1

See a solution process below:

Explanation:

We can use this rule for quadratics to expand this expression:

`(color(red)(a) + color(blue)(b))^2 = (color(red)(a) + color(blue)(b))(color(red)(a) + color(blue)(b)) = color(red)(a)^2 + 2color(red)(a)color(blue)(b) + color(blue)(b)^2`

Let: `color(red)(a) = color(red)(6xy)`

Let: `color(blue)(b) = color(blue)(8)`

Substitute and write the expression as:

`(color(red)(6xy) + color(blue)(8))^2 =>`

`(color(red)(6xy) + color(blue)(8))(color(red)(6xy) + color(blue)(8)) =>`

`color(red)((6xy))^2 + (2 * color(red)(6xy) * color(blue)(8)) + color(blue)(8)^2 =>`

`36x^2y^2 + 96xy + 64`