How do you simplify the product #(x^2 + x - 1)(x + 1)# and write it in standard form?
1 Answer
Sep 5, 2016
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.
