Question

How do you find the product `(2+x)(2-x)`?

Answer 1

See the entire solution process below:

Explanation:

This is a special case described by:

`(a + b)(a - b) = a^2 - b^2`

Letting `a` equal `2` and `b` equal `x` and substituting gives:

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

We can also multiply the two terms using this process. To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.

`(color(red)(2) + color(red)(x))(color(blue)(2) - color(blue)(x))` becomes:

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

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

We can now combine like terms:

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

`4 + 0 - x^2`

`4 - x^2`

Answer 2

Use the distributive property and then combine common terms.
`( 4 - x^2)`

Explanation:

Use the distributive property to multiply the parenthesis. This gives.

`(2 + x) xx ( 2-x) = 2 xx (2 -x) + x xx ( 2-x)` Multiplying across gives

`2 xx ( 2 -x ) + x xx (2-x) = 4 - 2x + 2x - x^2` Combining like terms

`4 - x^2`