How do you expand and simplify #(x^2-1)(x-1)#?

2 Answers
Tony B
May 12, 2018

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

Explanation:

#color(blue)((x-1))color(green)((x^2-1))#

Multiply everything in the right hand bracket by everything in the left one.

#color(green)( color(blue)(x)(x^2-1)color(blue)(-1)(x^2-1) )larr# Notice the minus follows the 1.

#color(white)("d")x^3-xcolor(white)("ddd")-x^2+1#

#color(white)("d")#

#color(white)("d")x^3-x^2-x+1#

Jim G.
May 12, 2018

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

Explanation:

#"each term in the second factor is multiplied by each"#
#"term in the first factor"#

#rArr(color(red)(x^2-1))(x-1)#

#=color(red)(x^2)(x-1)color(red)(-1)(x-1)#

#=(color(red)(x^2)xx x)+(color(red)(x^2)xx-1)+(color(red)(-1)xx x)+(color(red)(-1)xx-1)#

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

#=x^3-x^2-x+1#

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