Question

How do you multiply `(7w - 3u - 6) ( 7w + 2)`?

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)(7w) - color(red)(3u) - color(red)(6))(color(blue)(7w) + color(blue)(2))` becomes:

`(color(red)(7w) xx color(blue)(7w)) + (color(red)(7w) xx color(blue)(2)) - (color(red)(3u) xx color(blue)(7w)) - (color(red)(3u) xx color(blue)(2)) - (color(red)(6) xx color(blue)(7w)) - (color(red)(6) xx color(blue)(2))`

`49w^2 + 14w - 21uw - 6u - 42w - 12`

We can now group and combine like terms:

`49w^2 + 14w - 42w - 21uw - 6u - 12`

`49w^2 + (14 - 42)w - 21uw - 6u - 12`

`49w^2 + (-28)w - 21uw - 6u - 12`

`49w^2 - 28w - 21uw - 6u - 12`

Answer 2

Basically, use the distributive property of multiplication and after the multiplication is done, combine the same variables and simplify them.

Explanation:

It is the use of the distributive properties of multiplication (since the concepts are almost the same in Algebra) and simplifying them altogether.

#(7w - 3u - 6)(7w+2) = 49w^2 -21uw -42w +14w - 6u -12 = 49w^2 - 21uw -28w - 6u -12 #