x Plus 1 Cube Expand Formula

x plus 1 cube expand formula

Before moving on with the x plus 1 cube expand formula, you must gain knowledge about a binomial. An algebraic expression that involves exactly two terms is called a binomial.

The x plus 1 cube expand formula has been identified as a particular algebraic identity formula that is implemented in solving a cube of a specific kind of binomial. The formula (x+1)³ is mathematically expanded if we multiply (x+1) three times. 

To further simplify, this formula combines the identical terms once the multiplication is complete, and also arranges the similar variables together. Eventually, let us arrange the algebraic expression following decreasing order of the power (exponential power).

What is x plus 1 cube expand formula?

The formula: (x+1)³ = x³ + 3x² + 3x + 1

On expanding the x plus 1 cube formula we get, (x+1)³ = (x+1) (x+1) (x+1)

Simplification of x plus 1 cube expand formula

The x plus 1 cube formula is proved or mathematically verified by multiplying the term (x+1) thrice. In the next section, we will notice how this works.

(x+1)³ = (x+1) (x+1) (x+1)

Or, (x+1)³ = (x+1) (x² + 1 + x + x)

= (x² + 2x + 1) (x+1) 

= x³ + x² + 2x² + 2x + 2 + x + 1

= x³ + 3x² + 3x + 1

So, we arrive at the conclusion that (x+1)³ = x³ + 3x² + 3x + 1

Solved examples

1. Expand the mathematical expression (m + 1)³

Solution: Implementing the x plus 1 cube expand formula: (x+1)³ = x³ + 3x² + 3x + 1

We replace x with the term m

∴ (m+1)³ = m³ + 3m² + m + 1

Answer: Expanded form of (m + 1)³ is m³ + 3m² + m + 1.

2. Expand (1+u)³

Solution: Again let us induce the (x+1)³ expand the formula to solve this problem.

(x+1)³ = x³ + 3x² + 3x + 1

Comparing and replacing the variables we get,

(1+u)³ = u³ + 3u² + u + 1

Answer: Expanded form of (1 + u)³ is u³ + 3u² + u + 1.