Using binomial theorem write down the expansions of the following… - Vidyadip

Question

Using binomial theorem write down the expansions of the following:
$\Big(\text{ax}-\frac{\text{b}}{\text{x}}\Big)^6$

✓

Answer

The expansion of $(x + y)^n $ has $n + 1$ terms so the expansion of $\Big(\text{ax}-\frac{\text{b}}{\text{x}}\Big)^6$has $7$ term Using binomial theorem to expand, we get
$\Big(\text{ax}-\frac{\text{b}}{\text{x}}\Big)^6={^6\text{C}}_0(\text{ax})^6\Big(\frac{\text{b}}{\text{x}}\Big)-{^6\text{C}}_1(\text{ax})^5\Big(\frac{\text{b}}{\text{x}}\Big)+{^6\text{C}}_2(\text{ax})^4\Big(\frac{\text{b}}{\text{x}}\Big)^2\\-{^6\text{C}}_3(\text{ax})^3\Big(\frac{\text{b}}{\text{x}}\Big)^3+{^6\text{C}}_4(\text{ax})^2\Big(\frac{\text{b}}{\text{x}}\Big)^4-{^6\text{C}}_5(\text{ax})\Big(\frac{\text{b}}{\text{x}}\Big)^5+{^6\text{C}}_6(\text{ax})^0\Big(\frac{\text{b}}{\text{x}}\Big)^6$
$=\text{a}^6\text{x}^6-6\text{a}^5\text{x}^5\frac{\text{b}}{\text{x}}+15\text{a}^4\text{x}^4\frac{\text{b}^2}{\text{x}^2}\\-20\text{a}^3\text{b}^3+15\text{a}^2\frac{\text{b}^4}{\text{x}^2}-6\text{a}\frac{\text{b}^5}{\text{x}}^4+\frac{\text{b}^6}{\text{x}^6}$
$=\text{a}^6\text{x}^6-6\text{a}^5\text{x}^4\text{b}\frac{\text{b}}{\text{x}}+15\text{a}^4\text{b}^2\text{x}^2-20\text{a}^3\text{b}^3+15\frac{\text{a}^2\text{b}^4}{\text{x}^2}-6\frac{\text{ab}^5}{\text{x}^4}+\frac{\text{b}^6}{\text{x}^6}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "3 Marks Question" from Binomial Theorem→Binomial Theorem — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

If $\frac{\text{a}+\text{bx}}{\text{a}-\text{bx}}=\frac{\text{b}+\text{cx}}{\text{b}-\text{cx}}=\frac{\text{c}+\text{dx}}{\text{c}-\text{dx}}(\text{x}\neq0),$ then show that a, b, c and d are in G.P.

If $a_1, a_2, a_3, ..., an$ are in$ A.P.,$ where $a_i > 0$ for all $i,$ show that:
$\frac{1}{\sqrt{\text{a}_1}+\sqrt{\text{a}_2}}+\frac{1}{\sqrt{\text{a}_2}+\sqrt{\text{a}_3}}+....+\frac{1}{\sqrt{\text{a}_{\text{n}-1}}+\sqrt{\text{a}_\text{n}}}=\frac{\text{n}-1}{\sqrt{\text{a}_1}+\sqrt{\text{a}_\text{n}}}$

Find the eccentricity of an ellipse whose latus-rectum ishalf of its minor axis

Solve the following system of equations in R.
$5\text{x} - 7 < 3(\text{x} + 3), 1-\frac{3\text{x}}{2}\geq\text{x}-4$

The longest side of a triangle is three times the shortest side and third side is 2 cm shorter than the longest side if the perimeter of the triangles at least 61 cm, find the minimum length of the shortest-side.

Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow3}\frac{\text{x}^2-4\text{x}+3}{{\text{x}^2}-2\text{x}-3}$

Differentiate the following functions with respect to x:$\frac{2^\text{x}\cot\text{x}}{\sqrt{\text{x}}}$

In a survey it was found that 21 people liked product A, 26 liked product B and 29 liked product C. If 14 people liked products A and B, 12 people liked products C and A, 14 people liked products B and C and 8 liked all the three products. Find how many liked product C only?

$\text { If } u =\{1,2,3,4,5,6,7,8,9,10,12,24\}$
$A =\{ x : x \text { is prime and } x \leq 10\}$
$B =\{ x : x \text { is a factor of } 24\}$
Verify the following result
$i. A - B = A \cap B^{\prime}$
$ii. (A \cup B)^{\prime}=A^{\prime} \cap B^{\prime}$
$iii. (A \cap B)^{\prime}=A^{\prime} \cup B^{\prime}$

Prove that: $\tan8\text{x}-\tan6\text{x}-\tan2\text{x}=\tan8\text{x}\tan6\text{x}\tan2\text{x}$