Book Online Demo

Check Your IQ

Courses

Class - 11 JEE Course Class - 11 NEET Course Class - 12 JEE Course Class - 12 NEET Course Dropper JEE Course Dropper NEET Course Class - 10 Foundation JEE Course Class - 10 Foundation NEET Course Class - 10 CBSE Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

What is the formula for $a^{3} - b^{3}$ ?

see full answer

Want to Fund your own JEE / NEET / Foundation preparation ??

Take the SCORE scholarship exam from home and compete for scholarships worth ₹1 crore!*

An Intiative by Sri Chaitanya

{(a - b)}^{3} + 3 ab (a - b)

{(a - b)}^{3} - 3 ab (a - b)

{(a - b)}^{3} + 3 ab (a + b)

{(a - b)}^{3} - 3 ab (a + b)

answer is A.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

Formula given:

a^{3} - b^{3}

.
Now, we can clearly see that the power of both the terms ‘a’ and ‘b’ in the expression

a^{3} - b^{3}

is 3 and there is a minus sign between the terms. So, let us consider the difference (a – b). Now, multiplying (a – b) three times with itself, we have,
⇒(a−b)(a−b)(a−b) =

{(a - b)}^{3}

⇒

{(a - b)}^{3}

= (a−b)(a−b)(a−b)
Multiplying the terms in the R.H.S by taking two at a time, we get,
⇒

{(a - b)}^{3}

= (

a^{2}

−ab−ba+

b^{2}

)(a−b)
⇒

{(a - b)}^{3}

= (

a^{2}

−2ab+

b^{2}

)(a−b)
Now, multiplying and simplifying the remaining term in the R.H.S, we get,
⇒

{(a - b)}^{3}

= (

a^{3}

−

a^{2}

b−2

a^{2}

b+2

a^{2}

b^{2}

a−

b^{3}

)(a−b)
⇒

{(a - b)}^{3}

= =(

a^{3}

−3

a^{2}

b+3a

b^{2}

−

b^{3}

)
⇒

{(a - b)}^{3}

= (

a^{3} - b^{3}

) +3a

b^{2}

−3

a^{2}

b
⇒ (

a^{3} - b^{3}

) =

{(a - b)}^{3}

−3

a^{2}

b+3a

b^{2}

⇒ (

a^{3} - b^{3}

) =

{(a - b)}^{3}

+3ab (a-b)
So, the above expression is the required formula for the provided expression (

a^{3} - b^{3}

Watch 3-min video & get full concept clarity

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Books for IIT JEE

Best Books for NEET

🔥 Start Your JEE/NEET Prep at Just ₹1999 / month - Limited Offer! Check Now!

Get Expert Academic Guidance – Connect with a Counselor Today!