Question

Find the third term in the expansion of (a+b)^9 in the simplest form

Answer 1

Answer:

$The\ third\ term\ is\ \boxed{36a^7b^2}$

Step-by-step explanation:

$\left(\begin{array}{c}9\\ 1\end{array}\right)=\dfrac{9}{1} =9\\\\\left(\begin{array}{c}9\\ 2\end{array}\right)=\dfrac{9*8}{2*1} =36\\\\\\(a+b)^9=a^9+\left(\begin{array}{c}9\\ 1\end{array}\right)a^8b+\left(\begin{array}{c}9\\ 2\end{array}\right)a^7b^2+....+b^9\\\\\\The\ third\ term\ is\ \boxed{36a^7b^2}$

Answer 2

The third term will be "36a⁷b²".

The given expression is:

• $(a+b)^9$

According to the question,

→ $\binom{9}{1} = \frac{9}{1}$

        $= 9$

→ $\binom{9}{2} = \frac{9\times 8}{2\times 1}$

        $= \frac{72}{2}$

        $= 36$

Now,

→ $(a+b)^9 = a^9+\binom{9}{1}a^8b+\binom{9}{2}a^7b^2+...+b^9$

hence,

The third term is "$36a^7b^2$".

Thus the approach above is appropriate.

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