Question

3x^2-4x-(x-2)^2 written as a simplified polynomial in standard form

Answer 1

You have the following algebraic expression:

`3x^2-4x-(x-2)^2`

In order to simplify the previous expression you first expand the third term of the polynomial, that is, you expand the term (x-2)². In order to make the expansion, you use the following notable product:

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

The, by taking into account the previous identity you obtain:

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

Next, you replace the last result into the given polynomial, as follow:

`3x^2-4x-(x^2-4x+4)`

Eliminate parenthesis by using the rule for multiplication of signs:

`3x^2-4x-x^2+4x-4`

and finally, you simplify like terms:

`3x^2-x^2-4x+4x-4=2x^2-4`

Hence, the simplified expression is 2x² - 4