a 3 - b 3 is always divisible by: Options: A . &nbsp a - b B . &nbsp a × b C . &nbsp a + b D . &nbsp 2a + b

a3 - b3 is always divisible by:

Question

$a^{3}$ - $b^{3}$ is always divisible by:

Options:

A . a - b

B . a × b

C . a + b

D . 2a + b

Answer: Option A
:
A

Take $a = 2$ and $b = 1$ and check.
Alternatively, we know the algebraic identity,

$a^{3} - b^{3} = (a - b) (a^{2} + 2 a b + b^{2}$ )

Hence , we can see that $(a - b)$ is a factor of $a^{3}$ - $b^{3}$
Thus, $a^{3}$ - $b^{3}$ is divisible by $(a - b)$

Was this answer helpful ?

Next Question

Question 1. What is the minimum number that should be multiplied with 360 in order to make it a perfect cube ? ....

Question 2. The volume of a closed cubical tank is 1331 cubic metres. Find the cost of painting its complete surface are....area from outside at the rate of ₹ 10 per square meter.

Question 3. What is the sum of the cubes of the first 7 natural numbers? ....

Question 4. If the value of (a3−b3a3+b3) when a = 7 and b = 2 is 335p, then p is 321. ....

Question 5. The units digit in the expansion of 163 is ___ ....

Question 6. The number of students in class 20 minutes ago was 729 . If the number of students joining the class tr....of the number of students joining after 40 minutes from now?

Question 7. The difference of cubes of two consecutive numbers is always divisible by 3. ....

Question 8. m3 ≥ m2 . To satisfy this condition, m can be ....

Question 9. What is the units digit of the cube of the number whose unit digit is 7? ....

Question 10. What is the value of 3√−8−3√−216 ? ....

Chapter 1 - GLOBAL STEEL SCENARIO & INDIAN STEEL INDUSTRY Part 1 : (13-04-2024) INDUSTRY AND COMPANY AWARENESS (ICA)

Direction Sense Test Part 1 Reasoning (Hindi)

Chapter 1 - RMHP / OHP / OB & BP Part 1 : (14-02-2024) GPOE

Cube & Cuboid Part 1 Reasoning (Hindi)

Data Interpretation (DI) Basic Concept Reasoning (Hindi)

Counting Figures Part 1 Counting Of Straight Lines Reasoning (Hindi)

Sail E0 free webinar Webinars

Real Numbers Part 7 Class 10 Maths

Real Numbers Part 1 Class 10 Maths

Polynomials Part 1 Class 10 Maths

DSP Combined 1 Free Revision Test SAIL JO E-0

GPOE / GPA Combined 1 Free Revision Test SAIL JO E-0

BSP Plant Specific Review Test SAIL JO E-0

BSL Combined 1 Free Revision Test SAIL JO E-0

GFM Combined 1 Free Revision Test SAIL JO E-0