Expand the binomial (x-(4)/(5))^(2)

Question

Expand the binomial

`(x-(4)/(5))^(2)`

Answer 1

`(x- (4)/(5))^(2) = x^2 -(8)/(5)x + (16)/(25)`

Explanation:

You have two methods to expand this binomial.

Method 1

If you have the expression:

`(x- (4)/(5))^(2)`

You can write the expression it in the following way:

`(x-(4)/(5))^(2)=(x-(4)/(5))(x-(4)/(5))`

Then, apply the distributive property:

`(x-(4)/(5))(x-(4)/(5)) = x^2 -(4)/(5)x -(4)/(5)x+ ((4)/(5))(4)/(5)`

Simplify the expression:

`(x-(4)/(5))^2= x^2 -(8)/(5)x+ ((16)/(25))`

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Method 2

For any expression of the form:

`(a-b)^2`

Its expanded form will be:

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

If

`a = x`

`b =(4)/(5)`

`(x- (4)/(5))^(2) = x^2 - 2x(4)/(5) + ((4)/(5))^2`

`(x- (4)/(5))^(2) = x^2 -(8)/(5)x + (16)/(25)`