Question

What is the first term in this expansion?

1.) 2x^15
2.) 2^15x^15
3.) 10y^15
4.) 10^15y^15

Answer 1

2¹⁵x¹⁵ (2nd option)

Explanation:

When you expand (2x+10y)¹⁵ you would get:

32,768x¹⁵ + 2,457,600x¹⁴y + 86,016,000x¹³y² + 1,863,680,000x¹²y³+

27,955,200,000x¹¹y⁴+307,507,200,000x¹⁰y⁵ + 307,507,200,000x¹⁰y⁵ + ... so on and so forth.

Since you are not interested in anything else but the first term, observe that the first term is:

32,768x¹⁵

That is equal to: 2¹⁵x¹⁵

What happened there is you need to distribute the exponent to the coefficient of the term as well, so you need to distribute it to 2 as well.