a3 + b3 Formula Proof
The sum of cube formula or a3 + b3 formula is proved by solving the RHS part of the formula and then simplifying the same to make it equal to the LHS. The a3 + b3 formula is,
a3 + b3 = (a + b)(a2 β ab + b2)
RHS = (a + b)(a2 β ab + b2)
Using the Distributive Property of Multiplication, we have
RHS = a(a2 β ab + b2)) + b(a2 β ab + b2)
β RHS = a3 β a2b + ab2 + a2b β ab2 + b3
β RHS = a3 β a2b + a2b + ab2 β ab2 + b3
β RHS = a3 β 0 + 0 + b3
β RHS = a3 + b3
β RHS = LHS
Hence proved.
(a + b)3 Formula
(a + b)3 formula is the formula that is used to expand the cube of sum of two numbers and the formula for the same is,
(a + b)3 = a3 + b3 + 3ab(a + b)
a3 + b3 Formula
a3 + b3 formula which is also called the sum of cubes formula, in algebra is the fundamental algebra formula that is used to find the sum of cubes of any two numbers without actually calculating their cubes. a3 + b3 formula is also used to find the factors of a3 + b3. This helps to simplify various algebraic expressions.
In this article, we will learn about, the a3 + b3 formula, factors of a3 + b3, examples, and others in detail.
Table of Content
- What is a3 + b3 Formula?
- What is Sum of Cubes Formula?
- a3 + b3 Formula Proof
- Examples on Sum of Cubes Formula
- a3 + b3 Formula β FAQs