Expand: (1-1 a )^3 - Vidyadip

Question

Expand: $\left(1-\frac{1}{a}\right)^3$

✓

Answer

Here, $A=1$ and $B=\frac{1}{a}$
$\begin{aligned}
\left(1-\frac{1}{a}\right)^3= & (1)^3-3(1)^2\left(\frac{1}{a}\right)+3(1)\left(\frac{1}{a}\right)^2-\left(\frac{1}{a}\right)^3 \\
& \ldots\left[(a-b)^3=a^3-3 a^2 b+3 a b^2-b^3\right] \\
= & \mathbf{1}-\frac{3}{a}+\frac{3}{a^2}-\frac{1}{a^3}
\end{aligned}$

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 Mark Question" from Expansion Formulae→Expansion Formulae — all question types→Maths STD 8 question papers→Maharashtra Board STD 8 question papers→Maharashtra Board question paper generator→

Similar questions

A car takes 5 hours to reach a destination by travelling at the speed of 60km/hr. How long will it take when the car travels at the speed of 75km/hr?

There is a continuous growth in population of a village at the rate of 5% per annum. If its present population is 9261, what it was 3 years ago?

After reading $\frac{7}{9}$ of a book, 40 pages are left. How many pages are there in the book?

Hari bought 20kg of rice at Rs. 36/kg and 25kg of rice at Rs. 32/kg He mixed the two varieties and sold the mixture at Rs. 38/kg Find his gain percent in the whole transaction.

A man is 10 times older than his grandson. He is also 54 years older than him. Find their present ages.

Which of the following numbers are cubes of negative integers.
$-64$

Factorise: $24 a^3+81 b^3$

Find the area of a trapezium whose parallel sides are 38.7 cm and 22.3 cm , and the distance between them is 16 cm .

Find the (i) curved surface area (ii) total surface area and (iii) volume of a right circular cylinder whose height is 15cm and the radius of the base is 7cm.

Evaluate $\sqrt{3}$ correct up to two places of decimal.