Answer:
The most simplified form is [tex]3 x^2-26 x+73[/tex], on step one she has [tex]3 (x-5)^2+4 x-2[/tex] and on step 2 she has [tex]3 (x^2-10x+25)+4 x-2[/tex]
Step-by-step explanation:
In order to simplify expressions we need to follow the order of operations, with acronym PEMDAS, that stands for Parenthesis first, then exponents, then multiplication or division and finally addition or subtraction.
Step 1 Simplifying within the parenthesis.
Since the expression has parenthesis we need to work with that part first, so inside the parenthesis we can proceed combining like terms.
Like terms are expressions that share a property, for example 2x and -x they both have x so we can combine them while -6 and +1 have no x and are just numbers so we can combine those as well.
So we will have
[tex]3 (2x-6-x+1)^2+4 x-2=3 (x-5)^2+4 x-2[/tex]
Here 2x-x give us just x and -6+1 = -5
Step 2 Expanding the exponent.
In order to expand the exponent we can work with FOIL procedure.
[tex](x-5)^2 = (x-5)(x-5)[/tex]
So if we work with that procedure we will get
[tex](x-5)^2 = x^2-5x-5x+25[/tex]
Simplifying we get
[tex](x-5)^2 = x^2-10x+25[/tex]
That means the result of step 2 will be
[tex]=3 (x^2-10x+25)+4 x-2[/tex]
Working to get the most simplified form
After expanding we can distribute the 3 in front to get
[tex]=3x^2-30x+75+4 x-2[/tex]
Lastly we can combine like terms to get
[tex]=3 x^2-26 x+73[/tex]
And that will be the most simplified form.
