To determine which row of Pascal's triangle to use for expanding [tex]\((2x + 10y)^{15}\)[/tex], we need to find the row that corresponds to the exponent of the expression.
In Pascal's triangle:
- The rows are indexed starting from 0.
- Row [tex]\( n \)[/tex] corresponds to the expansion of [tex]\( (a + b)^n \)[/tex].
Given the expression [tex]\((2x + 10y)^{15}\)[/tex]:
- The exponent is 15.
- Therefore, you would use row 15 of Pascal's triangle for the expansion.
Next, to determine the number of terms in the expansion:
- In a binomial expansion [tex]\((a + b)^n\)[/tex], the number of terms is given by [tex]\( n + 1 \)[/tex].
For the given expression [tex]\((2x + 10y)^{15}\)[/tex]:
- The exponent [tex]\( n \)[/tex] is 15.
- So, the number of terms in the expansion is [tex]\( 15 + 1 = 16 \)[/tex] terms.
Thus, the answers are:
- Row [tex]\( \boxed{15} \)[/tex] of Pascal's triangle should be used.
- The expansion contains [tex]\( \boxed{16} \)[/tex] terms.
