Answer:
[tex](x- \frac{2}{5})^{2} = x^2 -\frac{4}{5}x + \frac{4}{25}[/tex]
Step-by-step explanation:
You have two methods to expand this binomial.
Method 1
If you have the expression:
[tex](x- \frac{2}{5})^{2}[/tex]
You can write the expression it in the following way:
[tex](x-\frac{2}{5})^{2}=(x-\frac{2}{5})(x-\frac{2}{5})[/tex]
Then, apply the distributive property:
[tex](x-\frac{2}{5})(x-\frac{2}{5}) = x^2 -\frac{2}{5}x -\frac{2}{5}x+ (\frac{2}{5})\frac{2}{5}[/tex]
Simplify the expression:
[tex](x-\frac{2}{5})^2= x^2 -\frac{4}{5}x+ (\frac{4}{25})[/tex]
---------------------------------------------------------------------------------------
Method 2
For any expression of the form:
[tex](a-b)^2[/tex]
Its expanded form will be:
[tex](a-b)^2= a^2 -2ab + b^2[/tex]
If
[tex]a = x[/tex]
[tex]b =\frac{2}{5}[/tex]
[tex](x- \frac{2}{5})^{2} = x^2 - 2x\frac{2}{5} + (\frac{2}{5})^2[/tex]
[tex](x- \frac{2}{5})^{2} = x^2 -\frac{4}{5}x + \frac{4}{25}[/tex]
