Q:

Expand the binomial[tex](x-\frac{4}{5})^{2}[/tex]

Accepted Solution

A:
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 Β 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]