Question

Find the values of the following polynomials at $a=-2$ and $b=3$.
(i) $a^3-3a^{2}b+3a{b}^2-b^3$
(ii) $a^2+b^2-ab-b^2-a^2$

Answer 1

When $a=-2$ and $b=3$,

$a^3-3a^{2}b+3a{b}^2-b^3=(-2{)}^3-3(-2{)}^2\left(3\right)+3(-2)(3{)}^2-3^3$
$=-8-3\left(4\right)\left(3\right)+3(-2)\left(9\right)-27$
$=-8-36-54-27$
$=-125$

$a^2+b^2-ab-b^2-a^2=(-2{)}^2+3^2-(-2\times 3)-3^2-(-2{)}^2$
$=4+9-(-6)-9-4$
$=4+9+6-9-4$
$=6$