Question

Which polynomial is the product of (x+2) and (x+2)?

Answer 1

`x^2 + 4x + 4`

Explanation:

A product is the result of multiplication. So, to solve this problem we must multiply `(color(red)(x+2))` by `(color(blue)(x+2))` or

`(color(red)(x+2))(color(blue)(x+2))`

This is done by cross multiplying the terms in the parenthesis on the left by each term in the parenthesis on the right:

`(color(red)(x) * color(blue)(x)) + (color(red)(x) * color(blue)(2)) + (color(red)(2) * color(blue)(x)) + (color(red)(2) * color(blue)(2)) ->`

`x^2 + 2x + 2x + 4`

Now, we can combine like terms to obtain the final polynomial.

`x^2 + (2 + 2)x + 4`

`x^2 + 4x + 4`