Answer:[tex](x- \frac{4}{5})^{2} = x^2 -\frac{8}{5}x + \frac{16}{25}[/tex]Step-by-step explanation:You have two methods to expand this binomial.
Method 1 If you have the expression:
[tex](x- \frac{4}{5})^{2}[/tex]
You can write the expression it in the following way:
[tex](x-\frac{4}{5})^{2}=(x-\frac{4}{5})(x-\frac{4}{5})[/tex]
Then, apply the distributive property:
[tex](x-\frac{4}{5})(x-\frac{4}{5}) = x^2 -\frac{4}{5}x -\frac{4}{5}x+ (\frac{4}{5})\frac{4}{5}[/tex]
Simplify the expression:
[tex](x-\frac{4}{5})^2= x^2 -\frac{8}{5}x+ (\frac{16}{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{4}{5}[/tex]
[tex](x- \frac{4}{5})^{2} = x^2 - 2x\frac{4}{5} + (\frac{4}{5})^2[/tex]
[tex](x- \frac{4}{5})^{2} = x^2 -\frac{8}{5}x + \frac{16}{25}[/tex]