About Sum of Cubes Formula
The sum of cubes formula is used to calculate the addition of two polynomials, a3 + b3. Let's look at several solved instances to learn more about the sum of cubes formula. When solving algebraic expressions of various types, this factoring formula comes in handy. This formula is also simple to remember and may be done in a matter of minutes. The change in cubes formula is also pretty similar.
Let's take it a step further and figure out what it means when someone says "sum of cubes." The formula for the sum of cubes is as follows:
a3 + b3 = (a + b)(a2 - ab + b2)
where,
- a - first variable
- b - second variable
a3 + b3 = (a + b)(a2 - ab + b2)
Proof of Sum of Cubes Formula
Verify that sum of cubes formula that is,
a3 + b3 = (a + b)(a2 - ab + b2)
prove here LHS = RHS.
LHS = a3 + b3
On Solving RHS term :-
= (a + b) (a2 - ab + b2)
On multiplying a & b separately with (a2 + ab + b2) we get
= a (a2 - ab + b2) + b(a2 - ab + b2)
= a3 - a2b + ab2 + a2b - ab2 + b3
= a3 - a2b + a2b + ab2- ab2 + b3
= a3 - 0 + 0 + b3
= a3 + b3
Hence proved, LHS = RHS
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