Question

Please help 6.Simplify and put in standard form: (2x5+x3−3x4−x+8)−(7 x 5+2x4−12+6x−5 x 3+x2)

Answer 1

We are given this:
$(2 x^{5} + x^{3}-3 x^{4} -x+8)-(7 x^{5} +2 x^{4} - 12+6x-5 x^{3} + x^{2} )$

First step is to get rid of brackets. There is no sign in front of first brackets, so we do not change the sign. In front of second brackets there is negative sign so we need to change sign for each term inside of those brackets.
$2 x^{5} + x^{3}-3 x^{4} -x+8-7 x^{5} -2 x^{4} + 12-6x+5 x^{3} - x^{2}$

Next step is to group terms with same exponent in descending order.
$2 x^{5} -7 x^{5} -3 x^{4}-2 x^{4}+ x^{3} +5 x^{3}- x^{2}-x-6x+8 + 12$

Now we add or substract terms with same exponent.

$-5 x^{5} -5 x^{4}+ 6x^{3}- x^{2}-7x+20$

Standard form means ordering terms in a descending order of an exponent.