Question

How do you find the product `(3a^2+7b)(3a^2-7b)`?

Answer 1

See a solution process below:

Explanation:

This is a special case quadratic:

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

Let `color(red)(x) = color(red)(3a^2)` and let `color(blue)(b) = color(blue)(-7b)`

Substituting gives:

`(color(red)(3a^2) + color(blue)(-7b))(color(red)(3a^2) - color(blue)(-7b)) = color(red)((3a^2))^2 - color(blue)((-7b))^2 = 9a^4 - 49b^2`