A sum of cubes is **a two-term expression where both terms are cubes** and each term has the same sign. It is factored according to the following formula: a3 + b3 = (a + b) (a2 – ab + b2) How can you determine if an expression can be factored as a sum of cubes? .

Contents

## What is Cube formula?

Length = Breadth = Height = a. Thus, the measure of each edge of the cube = a. Therefore, the volume of cube formula is a × a × a = a^{3}. It is to be noted that the number obtained using cube formula is the perfect cube number.

## How do you Factorise a cube?

An expression of the form a^{3} + b^{3} is called a sum of cubes. The factored form of a^{3} + b^{3} is (a + b)(a^{2} – ab + b^{2}): (a + b)(a^{2} – ab + b^{2}) = a^{3} + a^{2}b – a^{2}b – ab^{2} + ab^{2} + b^{3} = a^{3} – b^{3}. For example, the factored form of 64x^{3} + 125 (a = 4x, b = 5) is (4x + 5)(16x^{2} – 20x + 25).

## What is the sum of cubes of first n natural numbers?

We know that sum of cubes of first n natural numbers is = (n(n+1)/2)^{2}.

## How do you write 2 cubed?

2 cubed is 2^{3} = 2×2×2 = 8. The term “cube” can be remembered because there are three dimensions in a cube (height, width, and depth) and the number being cubed appears three times in the calculation.

## What is two cube difference?

The difference of two cubes is equal to the difference of their cube roots times a trinomial, which contains the squares of the cube roots and the opposite of the product of the cube roots.