Sum of Cubes Formula
Cube of a number is the number multiplied by itself twice. The sum of the cube is the formula that is the formula for a3 + b3 and its formula is added below,
a3 + b3 = (a + b)(a2 – ab + b2)
The above formula is algebraic identity and that is used to find the sum of cubes formula.
Sum of Cube Formula Proof
This identity can be proved by multiplying the expressions on the right side and getting equal to the left side expression. Here is the proof of this identity.
Given Identity:
a3 + b3 = (a + b) (a2 – ab + b2)
Proof:
= RHS
= (a + b)(a2 – ab + b2)
= a(a2 – ab + b2)) + b(a2 – ab + b2)
= a3 – a2b + ab2 + a2b – ab2 + b3
= a3 – a2b + a2b + ab2 – ab2 + b3
= a3 + b3
= LHS
Hence proved.
Sum and Difference of Cubes
The sum and difference of cubes are algebraic formulas used to factor expressions of the form a3+b3 and a3−b3 respectively. These formulas are particularly useful in simplifying and solving polynomial equations.
It is the basic formula of algebra used to solve the sum of the cubes and the difference of the cubes without actually calculating the values of the cubes. The sum of the cubes of the polynomial is represented as, a3 + b3 whereas the difference of the cubes is represented as a3– b3. These algebraic expressions are easily factorized using various algebraic expressions without actually calculating the cubes.
In this article, we will learn about Sum of Cubes, Sum of Cubes Formula, Factoring Sum of Cubes, Difference of Cubes, Difference of Cubes Formula with examples in detail below.