# Expand Master and Build Polynomial Equations Calculator

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Expand (n + 2)2

Since (n + 2)2 is a binomial
Use the binomial theorem to expand this.

## Build binomial expansion

a(x + y)n = aΣ[k = 0 to n]C(n,k) xn-kyk
where
 C(n,k)  = n! k!(n - k)!

## Plug in values

n = 2, x = n, a = 1, and y = 2.
Expanding terms, we get:

## k = 0

C(2,0)x2-0y0 = C(2,0)x2y0

## C(2,0):

 C(2,0)  = 2! 0!(2 - 0)!

C(2,0) = 1
Click to see C(2,0)

## Simplify our expanded term:

C(2,0)x2y0 = C(2,0)(n)2 - 0(2)0
C(2,0)x2y0 = (1)(n)2(2)0
C(2,0)x2y0 = (1)(1)(1n2)(1)

## Group constants and powers

C(2,0)x2y0 = (1 * 1 * 1 * 1)(n2)
C(2,0)x2y0 = 1n2

## k = 1

C(2,1)x2-1y1 = C(2,1)x1y1

## C(2,1):

 C(2,1)  = 2! 1!(2 - 1)!

C(2,1) = 2
Click to see C(2,1)

## Simplify our expanded term:

C(2,1)x1y1 = C(2,1)(n)2 - 1(2)1
C(2,1)x1y1 = (2)(n)1(2)1
C(2,1)x1y1 = (1)(2)(1n)(2)

## Group constants and powers

C(2,1)x1y1 = (1 * 2 * 1 * 2)(n1)
C(2,1)x1y1 = 4n

## k = 2

C(2,2)x2-2y2 = C(2,2)x0y2

## C(2,2):

 C(2,2)  = 2! 2!(2 - 2)!

C(2,2) = 1
Click to see C(2,2)

## Simplify our expanded term:

C(2,2)x0y2 = C(2,2)(n)2 - 2(2)2
C(2,2)x0y2 = (1)(n)0(2)2
C(2,2)x0y2 = (1)(1)(1)(4)

## Group constants and powers

C(2,2)x0y2 = (1 * 1 * 1 * 4)(1)
Anything raised to a 0 power = 1
C(2,2)x0y2 = 4

## Build our answer:

(n + 2)2 = 1n2 + 4n + 4************ End Binomial Expansion ********************

1n2 + 4n + 4

### How does the Expand Master and Build Polynomial Equations Calculator work?

Free Expand Master and Build Polynomial Equations Calculator - This calculator is the ultimate expansion tool to multiply polynomials. It expands algebraic expressions listed below using all 26 variables (a-z) as well as negative powers to handle polynomial multiplication. Includes multiple variable expressions as well as outside multipliers.
Also produces a polynomial equation from a given set of roots (polynomial zeros). * Binomial Expansions c(a + b)x
* Polynomial Expansions c(d + e + f)x
* FOIL Expansions (a + b)(c + d)
* Multiple Parentheses Multiplications c(a + b)(d + e)(f + g)(h + i)

This calculator has 2 inputs.

### What 1 formula is used for the Expand Master and Build Polynomial Equations Calculator?

1. a(x + y)n = aΣ[k = 0 to n]C(n,k) xn-kyk

For more math formulas, check out our Formula Dossier

### What 6 concepts are covered in the Expand Master and Build Polynomial Equations Calculator?

FOIL
First Outside Inside Last - A method for multiplying two binomials
binomial
Polynomial which is the sum of two monomials
expand
expand master and build polynomial equations
polynomial
an expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable(s).