Cube + 3 X square + 3 X + 28 explain in the form of 3 Cube a cube plus b cube form
Answers
a Cube plus b Cube Formula :
In this section, we are going to see the formula for
a3 + b3
We already know the formula/expansion for (a + b)3.
That is,
(a + b)3 = a3 + b3 + 3ab(a + b)
Case 1 :
(a + b)3 = a3 + b3 + 3ab(a + b)
Subtract 3ab(a + b) from each side.
(a + b)3 - 3ab(a + b) = a3 + b3
Therefore, the formula for (a3 + b3) is
a3 + b3 = (a + b)3 - 3ab(a + b)
Case 2 :
From case 1,
a3 + b3 = (a + b)3 - 3ab(a + b)
a3 + b3 = (a + b)[(a + b)2 - 3ab]
a3 + b3 = (a + b)[a2 + 2ab + b2 - 3ab]
a3 + b3 = (a + b)(a2 - ab + b2)
Therefore, the formula for (a3 + b3) is
a3 + b3 = (a + b)(a2 - ab + b2)
So,
(a + b) and (a2 - ab + b2)
are the factors of (a3 + b3).
Note :
Based on our need, either we can use the formula in case 1 or in case 2 for (a3 + b3).