# How do you express #(x-5)^2# in standard form?

##### 1 Answer

#### Answer:

#### Explanation:

The standard form of a polynomial in one variable is a sum of terms in decreasing order of degree.

For brevity, terms with negative coefficients are usually written as subtractions rather than adding the additive inverses. That is, we would write

In order to express

#(x-5)^2 = (x-5)(x-5)#

#color(white)((x-5)^2) = overbrace((x)(x))^"First" + overbrace((x)(-5))^"Outside" + overbrace((-5)(x))^"Inside" + overbrace((-5)(-5))^"Last"#

#color(white)((x-5)^2) = x^2-5x-5x+25#

#color(white)((x-5)^2) = x^2-10x+25#

Alternatively, we can recognise a pattern and use it.

For example:

#(a+b)^2 = a^2+2ab+b^2#

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

So we could take the second of these and put

#(x-5)^2 = x^2-2(x)(5)+5^2#

#color(white)((x-5)^2) = x^2-10x+25#