How do you simplify the product #(x^2 + x - 1)(x + 1)# and write it in standard form?

1 Answer
Sep 5, 2016

Answer:

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

Explanation:

We must ensure that each term in the second bracket is multiplied by each term in the first bracket.
This can be done as follows.

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

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

distribute each set of brackets.

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

and now collect like terms

#rArrcolor(blue)(x^3)color(red)(+x^2)color(red)(+x^2)color(magenta)cancel(+x)color(magenta)cancel(-x)-1=x^3+2x^2-1#

#=x^3+2x^2-1" in standard form"#

Standard form means writing the expression beginning with the term which has the highest power of the variable. In this case #x^3# then the next term with the next highest power. In this case #+2x^2# and so on until the last term.