How do you use the binomial theorem to expand and simplify the expression 2(x-3)^4+5(x-3)^2?

Nov 30, 2017

$2 {x}^{4} - 24 {x}^{3} + 113 {x}^{2} - 246 x + 126$

Explanation:

The first term expansion:
$2 \left({x}^{4} - 4 \left(3\right) {x}^{3} + 6 \left({3}^{2}\right) {x}^{2} - 4 \left({3}^{3}\right) x + {3}^{4}\right)$
$= 2 {x}^{4} - 24 {x}^{3} + 108 {x}^{2} - 216 x + 81$

The second term expansion:
$5 \left({x}^{2} - 2 \left(3\right) x + {3}^{2}\right)$
$= 5 {x}^{2} - 30 x + 45$

$2 {x}^{4} - 24 {x}^{3} + 113 {x}^{2} - 246 x + 126$