Question

How do you factor `36u ^ { 2} + 60ux + 25x ^ { 2}`?

Answer 1

See a solution process below:

Explanation:

This is a special case of the quadratic:

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

Let `x^2 = 36u^2`; then `x = 6u`

Let `y^2 = 25x^2`; then `y = 5x`

Substituting gives:

`color(red)(36)color(red)(u)^2 + 60color(red)(u)color(blue)(x) + color(blue)(25)color(blue)(x)^2 = (color(red)(6u) + color(blue)(5x))(color(red)(6u) + color(blue)(5x)) = (color(red)(6u) + color(blue)(5x))^2`