Question

For the given term, find the binomial raised to the power, whose expansion it came from: 10a^3b^2. option a: (a+b)^5option b: (-a+b)^5 option c: (a+square root 5/3b)^4 option d: (5a+b)^2

Answer 1

Explanation

Expanding each option, we get:

$\begin{gathered} (a+b)^5=a^5+5a^4b+(10a^3b^2)+10a^2b^3+5ab^4+b^5, \\ (-a+b)^5=-a^5+5a^4b-10a^3b^2+10a^2b^3-5ab^4+b^5, \\ (a+\sqrt{\frac{5}{3}}b)^4=a^4+4\sqrt{\frac{5}{3}}a^3b+10a^2b^2+\frac{20}{3}\sqrt{\frac{5}{3}}ab^3+\frac{25b^{4}}{9}, \\ (5a+b)^2=25a^2+10ab+b^2. \end{gathered}$

From the expansions above, we see that the first one has the term +10a³b².

Answer

(a + b)⁵