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.

a cube plus b 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

Please follow and like us:

Leave a Reply

avatar
  Subscribe  
Notify of