Question

what is the difference of the polynomials?
$(x^{4}+x^{3}+x^{2}+x)-(x^{4}-x^{3}+x^{2}-x)$
$2x^{2}$
$2x^{3}+2x$
$x^{6}+x^{2}$
$2x^{6}+2x^{2}$

Explanation:

Step1: Distribute the negative sign

$(x^4 + x^3 + x^2 + x) - x^4 + x^3 - x^2 + x$

Step2: Combine like $x^4$ terms

$x^4 - x^4 + x^3 + x^3 + x^2 - x^2 + x + x = 0 + x^3 + x^3 + x^2 - x^2 + x + x$

Step3: Combine like $x^3$ terms

$0 + (1+1)x^3 + x^2 - x^2 + x + x = 2x^3 + x^2 - x^2 + x + x$

Step4: Combine like $x^2$ terms

$2x^3 + (1-1)x^2 + x + x = 2x^3 + 0 + x + x$

Step5: Combine like $x$ terms

$2x^3 + (1+1)x = 2x^3 + 2x$

Answer:

$\boldsymbol{2x^3 + 2x}$ (Option B)