If (a+3 b)=6, show that a^3+27 b^3+54 a b=216. - Vidyadip

Question

If $(a+3 b)=6$, show that $a^3+27 b^3+54 a b=216.$

✓

Answer

self

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 "[4 marks sum]" from Expansions→Expansions — all question types→MATHEMATICS STD 9 question papers→ICSE Board STD 9 question papers→ICSE Board question paper generator→

Similar questions

Find the fraction which becomes $\frac{1}{2}$ when its numerator is increased by 6 and is equal to $\frac{1}{3}$ when its denominator is increased by 7 .

In each of the following, one trigonometric ratio is given. Find the values of the other trigonometric. $\cot A =\frac{1}{11}$

Evaluate:$\sqrt{\frac{1}{4}}+(0.01)^{-\frac{1}{2}}-(27)^{\frac{2}{3}}$

In $\triangle ABC; AB = AC. P, Q,$ and $R$ are mid$-$points of sides $AB, AC,$ and $BC$ respectively.Prove that$: PR = QR$

If $(4 a+3 b)=10$ and $a b=2$, find the value of $\left(64 a^3+27 b^3\right)$.

Arrange the sides of the following triangles in an ascending order:$\triangle ABC, \angle A = 45^\circ , \angle B = 65^\circ .$

Find graphically, the vertices of the triangle whose sides have the equations $2y - x = 8; 5y - x = 14$ and $y - 2x = 1$ respectively. Take $1 \ cm = 1$ unit on both the axes.

The marks obtained by 40 students of a class in an examination are given below Present the data in the form of a frequency distribution using equal class-size, or such class being 10-15 (15 not included).
3, 20, 13, 1, 21, 13, 3 23, 16, 13, 18, 12, 5, 12, 5, 24, 9, 2, 7, 18, 20, 3, 10, 12, 7, 18, 2, 5, 7, 10, 16, 8, 16, 17, 8, 23, 21, 6, 23, 15

A man lends $Rs. 12,500$ at $12\%$ for the first year, at $15\%$ for the second year and at $18\%$ for the third year. If the rates of interest are compounded yearly ; find the difference between the $C.I.$ fo the first year and the compound interest for the third year.

The area between the circumference of two concentric circles is $2464\ cm^2.$ If the inner circle has a circumference of $132\ cm, $ calculate the radius of the outer circle.