Question

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

Answer 1

`2x^4-24x^3+113x^2-246x+126`

Explanation:

The first term expansion:
`2(x^4-4(3)x^3+6(3^2)x^2-4(3^3)x+3^4)`
`=2x^4-24x^3+108x^2-216x+81`

The second term expansion:
`5(x^2-2(3)x+3^2)`
`=5x^2-30x+45`

Add the 2 terms:
`2x^4-24x^3+113x^2-246x+126`