Question

How do you multiply `(ab + xy)(7ab + 9xy)`?

Answer 1

See a solution process below:

Explanation:

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

`(color(red)(ab) + color(red)(xy))(color(blue)(7ab) + color(blue)(9xy))` becomes:

`(color(red)(ab) xx color(blue)(7ab)) + (color(red)(ab) xx color(blue)(9xy)) + (color(red)(xy) xx color(blue)(7ab)) + (color(red)(xy) xx color(blue)(9xy))`

`7a^2b^2 + 9abxy + 7abxy + 9x^2y^2`

We can now combine like terms:

`7a^2b^2 + (9 + 7)abxy + 9x^2y^2`

`7a^2b^2 + 16abxy + 9x^2y^2`