Expand the following
(x + 8)3
Binomial Expansion
Since (x + 8)3 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 = 3, x = x, a = 1, and y = 8.
Expanding terms, we get:
k = 0
C(3,0)x3-0y0 = C(3,0)x3y0
C(3,0):
| C(3,0) = | 3! |
| 0!(3 - 0)! |
C(3,0) = 1
Click to see C(3,0)
Simplify our expanded term:
C(3,0)x3y0 = C(3,0)(x)3 - 0(8)0
C(3,0)x3y0 = (1)(x)3(8)0
C(3,0)x3y0 = (1)(1)(1x3)(1)
Group constants and powers
C(3,0)x3y0 = (1 * 1 * 1 * 1)(x3)
C(3,0)x3y0 = 1x3
k = 1
C(3,1)x3-1y1 = C(3,1)x2y1
C(3,1):
| C(3,1) = | 3! |
| 1!(3 - 1)! |
C(3,1) = 3
Click to see C(3,1)
Simplify our expanded term:
C(3,1)x2y1 = C(3,1)(x)3 - 1(8)1
C(3,1)x2y1 = (3)(x)2(8)1
C(3,1)x2y1 = (1)(3)(1x2)(8)
Group constants and powers
C(3,1)x2y1 = (1 * 3 * 1 * 8)(x2)
C(3,1)x2y1 = 24x2
k = 2
C(3,2)x3-2y2 = C(3,2)x1y2
C(3,2):
| C(3,2) = | 3! |
| 2!(3 - 2)! |
C(3,2) = 3
Click to see C(3,2)
Simplify our expanded term:
C(3,2)x1y2 = C(3,2)(x)3 - 2(8)2
C(3,2)x1y2 = (3)(x)1(8)2
C(3,2)x1y2 = (1)(3)(1x)(64)
Group constants and powers
C(3,2)x1y2 = (1 * 3 * 1 * 64)(x1)
C(3,2)x1y2 = 192x
k = 3
C(3,3)x3-3y3 = C(3,3)x0y3
C(3,3):
| C(3,3) = | 3! |
| 3!(3 - 3)! |
C(3,3) = 1
Click to see C(3,3)
Simplify our expanded term:
C(3,3)x0y3 = C(3,3)(x)3 - 3(8)3
C(3,3)x0y3 = (1)(x)0(8)3
C(3,3)x0y3 = (1)(1)(1)(512)
Group constants and powers
C(3,3)x0y3 = (1 * 1 * 1 * 512)(1)
Anything raised to a 0 power = 1
C(3,3)x0y3 = 512
Build our answer:
(x + 8)3 = 1x3 + 24x2 + 192x + 512
************ End Binomial Expansion ********************
Final Answer
1x3 + 24x2 + 192x + 512
You have 1 free calculations remaining
What is the Answer?
1x3 + 24x2 + 192x + 512
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)
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What 1 formula is used for the Expand Master and Build Polynomial Equations Calculator?
a(x + y)n = aΣ[k = 0 to n]C(n,k) xn-kykFor more math formulas, check out our Formula Dossier
What 6 concepts are covered in the Expand Master and Build Polynomial Equations Calculator?
FOILFirst Outside Inside Last - A method for multiplying two binomialsbinomialPolynomial which is the sum of two monomialsexpandexpand master and build polynomial equationspolynomialan expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable(s).Example calculations for the Expand Master and Build Polynomial Equations Calculator
Expand Master and Build Polynomial Equations Calculator Video
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