Question

which row of pascals triangle would you use to expand (2x + 10y)^15? row 10 row 12 row 15 row 25 how many terms are in this expansion? 16 terms what is the first term in this expansion? 2x^15 2^15x^15 10y^15 10^15y^15

Explanation:

Step1: Recall binomial expansion rule

The binomial expansion of \((a + b)^n=\sum_{k = 0}^{n}\binom{n}{k}a^{n - k}b^{k}\), and the coefficients of the binomial expansion \((a + b)^n\) are given by the \(n+1\) - th row of Pascal's triangle. For \((2x+10y)^{15}\), we use the 16 - th row of Pascal's triangle (since rows of Pascal's triangle are numbered starting from 0).

Step2: Find the first - term formula

In the binomial expansion \((a + b)^n\), when \(k = 0\), the term is \(\binom{n}{0}a^{n}b^{0}\). For \((2x+10y)^{15}\), \(a = 2x\), \(b = 10y\), and \(n = 15\). When \(k = 0\), the first - term is \((2x)^{15}=2^{15}x^{15}\).

Step3: Determine the number of terms

For the binomial expansion \((a + b)^n\), the number of terms is \(n + 1\). Since \(n=15\) for \((2x + 10y)^{15}\), the number of terms is \(15 + 1=16\).

Answer:

Which row of Pascal's triangle would you use to expand \((2x + 10y)^{15}\)? Row 16
What is the first term in this expansion? \(2^{15}x^{15}\)
How many terms are in this expansion? 16