Question

How do you multiply `(7b^2-3c)^2`?

Answer 1

See the entire solution process below:

Explanation:

We can rewrite this expression as:

`(7b^2 - 3c)(7b^2 - 3c)`

To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.

`(color(red)(7b^2) - color(red)(3c))(color(blue)(7b^2) - color(blue)(3c))` becomes:

`(color(red)(7b^2) xx color(blue)(7b^2)) - (color(red)(7b^2) xx color(blue)(3c)) - (color(red)(3c) xx color(blue)(7b^2)) + (color(red)(3c) xx color(blue)(3c))`

`49b^4 - 21b^2c - 21b^2c + 9c^2`

We can now combine like terms:

`49b^4 + (-21 - 21)b^2c + 9c^2`

`49b^4 - 42b^2c + 9c^2`