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} = a^{3} + 3a^{2}b + 3ab^{2} + b^{3}

From the above mentioned formula we can find out the result of **a cube plus b cube**. Keep a^{3} + b^{3} 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} – 3a^{2}b – 3ab^{2 }= a^{3} + b^{3}

(a + b)^{3} – 3ab (a + b) = a^{3} + b^{3}

a^{3} + b^{3 =} (a + b)^{3} – 3ab (a + b)

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

**Find the value of a**^{3}**+ b**^{3}**if ab = 7 and a + b = 3.**

Solution:

Given

ab = 7

a + b = 3

we know that,

a^{3} + b^{3 }= (a + b)^{3} – 3ab(a + b)

= 3^{3} – 3 x 7 x 3

= 27 – 63

= – 36

**Find the value of ab if a**^{3}**+ b**^{3}**is 245 and a + b = 5.**

Solution:

Given

a^{3} + b^{3} = 245

a + b = 5

we know that

a^{3} + b^{3 }= (a + b)^{3} – 3ab(a + b)

245 = 5^{3} – 3x ab x 5

245-125 = -15ab

120 = – 15ab

120/-15 = ab

Therefore, ab = -8

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