# A cube plus b cube formula

Do you know the formula for a cube plus b cube? This formula if you learn, it will be very useful while solving sums on algebra. Actually, a cube plus b cube formula can be derived from the formula a plus b whole cube.

I hope you know the formula of a plus b whole cube. If you don’t know first learn that formula because we can find the formula of a cube plus b cube very easily.

## Derivation of a cube plus b cube formula:

We know the formula

(a + b)3  =  a3 + 3a2b + 3ab2 + b3

From the above mentioned formula we can find out the result of a cube plus b cube. Keep a3 + b3 on one side of equation i.e. on either on right hand side or left hand side and remaining take it on other side.

(a + b)3 –  3a2b –  3ab2 = a3 + b3

(a + b)3 – 3ab (a + b) = a3 + b3

a3 + b3 = (a + b)3 – 3ab (a + b)

### Example problems on a cube plus b cube :

• Find the value of a3 + b3 if ab = 7 and a + b = 3.

Solution:

Given

ab = 7

a + b = 3

we know that,

a3 + b3 = (a + b)3 – 3ab(a + b)

=  33 – 3 x 7 x 3

= 27 – 63

= – 36

• Find the value of ab if a3 + b3 is 245 and a + b = 5.

Solution:

Given

a3 + b3 = 245

a + b = 5

we know that

a3 + b3 = (a + b)3 – 3ab(a + b)

245    =  53  –  3x ab x 5

245-125    = -15ab

120   = – 15ab

120/-15 = ab

Therefore, ab = -8