# What is the standard form of #y=(3-x)(x-1)^2#?

##### 1 Answer

Nov 29, 2017

#### Explanation:

#"expand the factors and collect like terms"#

#(x-1)^2=(x-1)(x-1)larrcolor(blue)"expand using FOIL"#

#(x-1)(x-1)=x^2-2x+1#

#"now multiply expansion by factor "(3-x)#

#(3-x)(x^2-2x+1)#

#"multiply each term in the second factor by each term"#

#"in the first factor"#

#color(red)(3)(x^2-2x+1)color(red)(-x)(x^2-2x+1)#

#=3x^2-6x+3-x^3+2x^2-xlarrcolor(blue)"collect like terms"#

#=-x^3+5x^2-7x+3larrcolor(red)"in standard form"#

#"to express a polynomial in "color(blue)"standard form"#

#"start with the term with the largest exponent of the variable"#

#"followed by terms of decreasing exponents in descending"#

#"order"#