# What is the standard form of  f=(x + 2)(x + 2)(x + y)(x - y) ?

Feb 22, 2018

${x}^{4} - {x}^{2} {y}^{2} + 4 {x}^{3} - 4 x {y}^{2} + 4 {x}^{2} - 4 {y}^{2}$

#### Explanation:

In order to write any polynomial in standard form, you look at the degree of each term. You then write each term in order of degree, from highest to lowest, left to write.
First of all you need to eliminate the brackets so, knowing that:

1. $\left(a + b\right) \left(a + b\right) = {\left(a + b\right)}^{2}$
2. $\left(a + b\right) \left(a - b\right) = {a}^{2} - {b}^{2}$
3. ${\left(a + b\right)}^{2} = {a}^{2} + 2 a b + {b}^{2}$

You have:

$\left(x + 2\right) \left(x + 2\right) \left(x + y\right) \left(x - y\right) = {\left(x + 2\right)}^{2} \left({x}^{2} - {y}^{2}\right) = \left({x}^{2} + 4 x + 4\right) \left({x}^{2} - {y}^{2}\right) = {x}^{4} - {x}^{2} {y}^{2} + 4 {x}^{3} - 4 x {y}^{2} + 4 {x}^{2} - 4 {y}^{2}$