Question

How do you factor `9x^4y^2 - z^6`?

Answer 1

See a solution process below:

Explanation:

This is a special case of a quadratic:

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

• Let `color(red)(a) = 3x^2y`; Then `color(red)(a)^2 = 9x^4y^2`

• Let `color(blue)(b) = z^3`; Then `color(blue)(b)^2 = z^6`

Substituting gives:

`color(red)(9x^4y^2) - color(blue)(z^6) =>`

`color(red)((3x^2y))^2 - color(blue)((z^3))^2 =>`

`(color(red)(3x^2y) + color(blue)(z^3))(color(red)(3x^2y) - color(blue)(z^3))`