Question

Hello, could you please help me? the binomial is (5x^3-x)^8

Answer 1

STEP - BY - STEP EXPLANATION

What to do?

Expand using binomial theorem.

Given:

`(5x^3-x)^8`

Applying Binomial theorem;

`(a+b)^n=\sum_{k\mathop{=}0}^nnC_ka^(n-k)b^k`

a=5x³ and b=-x

`(5x^3-x)^8=\sum_{k\mathop{=}0}^8\text{ }^8C_0(5x^3)^(8-k)(-x)^k`

Expand the summation.

Now, simplify the above.

`=390625x^(24)-625000x^(22)+`