To determine which row of Pascal's triangle is needed to expand [tex]\((2x + 10y)^{15}\)[/tex], we should note that the row number we select in Pascal's triangle corresponds to the exponent of the binomial expression.
In general, to expand [tex]\((a + b)^n\)[/tex], we use the [tex]\(n\)[/tex]th row of Pascal's triangle. The elements of this row provide the binomial coefficients for the expanded form.
Given the binomial expression [tex]\((2x + 10y)^{15}\)[/tex]:
- The exponent [tex]\(n\)[/tex] is [tex]\(15\)[/tex].
Thus, the correct row of Pascal's triangle to use for expanding [tex]\((2x + 10y)^{15}\)[/tex] is row [tex]\(15\)[/tex].
Therefore, the correct answer is:
row 15.
