Cube by Column method

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For finding the cube by column method use the following formula:-
(a + b) ³ = a ³ + 3a ² b + 3ab ² + b ³
In this method, first find the 2 digits of a number.

Example:
1) 32 ³ , so here the two digits are 3 and 2.
2) 46 ³ , two digits are 4 and 6.

Examples:-

1) Find 24 ³ .
Solution: Here two digits are 2 and 4.
a = 2, and b = 4. By using the column-method:-

Column I	Column II	Column III	Column IV
a3	3 x a2 x b	3 x a x b2	b3
23 = 8 + 5	3 x 22 x 4 = 48 + 10	3 x 2 x 42 = 96 + 6	43 = 64
13	58	102	4
13	8	2	4

∴ 24 ³ = 13824
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2) Find 42 ³ .
Solution: Here two digits are 4 and 2.
a = 4, and b = 2. By using the column-method:-

Column I	Column II	Column III	Column IV
a3	3 x a2 x b	3 x a x b2	b3
43 = 64 + 10	3 x 42 x 2 = 96 + 4	3 x 4 x 22 = 48 + 0	23 = 8
74	100	48	8
74	0	8	8

∴ 42 ³ = 74088

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Cube - Cube Roots

• Cube of Numbers
• Perfect- Cube
• Properties of - Cube
• Cube by Column method
• Negative numbers-cube
• Cube - of Rational numbers
• Cube-Root
• Finding cube-root by Prime Factorization
• Cube-root of Rational numbers
• Estimating cube-root

From column method to Exponents

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