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Created on: 2012-01-27

A sample problem solved by Quickmath web math solver

x^2+12*0^13*x = 6.25*10^26 equation solved | analyze techniques to multiply out a sum that comprises 5 terms; n*(n-1)*(n-2)*(n-3)*(n-4)

Command

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Expression

(2*a*c*x+2*c-d)^3

  1. A power. The base is a sum that contains 3 terms. The 1st term of the sum is a product that contains 4 factors. The 1st factor of the product is equal to two. The 2nd factor of the product is equal to a. The 3rd factor of the product is equal to c. The 4th factor of the product is equal to x. The 2nd term of the sum is equal to a product containing 2 factors. The 1st factor of the product is equal to two. The 2nd factor of the product is equal to c. The 3rd term of the sum is equal to negative d. The exponent is three.
  2. left parenthesis two multiplied by a times c multiplied by x plus two multiplied by c plus negative d right parenthesis exponentiated by three.

Result

8*a^3*c^3*x^3-12*a^2*c^2*d*x^2+24*a^2*c^3*x^2+6*a*c*d^2*x-24*a*c^2*d*x+24*a*c^3*x-d^3+6*c*d^2-12*c^2*d+8*c^3

  1. A sum consisting of 10 terms. The 1st term of the sum is equal to a product that comprises 4 factors. The 1st factor of the product is eight. The 2nd factor of the product is a power. The base is a. The exponent is three. The 3rd factor of the product is equal to a power. The base is c. The exponent is three. The 4th factor of the product is equal to a power. The base is x. The exponent is three. The 2nd term of the sum is equal to a negative product that consists of 5 factors. The 1st factor of the product is twelve. The 2nd factor of the product is a power. The base is a. The exponent is two. The 3rd factor of the product is equal to a power. The base is c. The exponent is two. The 4th factor of the product is d. The 5th factor of the product is a power. The base is x. The exponent is two. The 3rd term of the sum is a product consisting of 4 factors. The 1st factor of the product is twenty four. The 2nd factor of the product is a power. The base is a. The exponent is two. The 3rd factor of the product is equal to a power. The base is c. The exponent is three. The 4th factor of the product is a power. The base is x. The exponent is two. The 4th term of the sum is a product comprising 5 factors. The 1st factor of the product is six. The 2nd factor of the product is equal to a. The 3rd factor of the product is equal to c. The 4th factor of the product is a power. The base is d. The exponent is two. The 5th factor of the product is equal to x. The 5th term of the sum is a negative product of 5 factors. The 1st factor of the product is twenty four. The 2nd factor of the product is a. The 3rd factor of the product is equal to a power. The base is c. The exponent is two. The 4th factor of the product is d. The 5th factor of the product is equal to x. The 6th term of the sum is a product comprising 4 factors. The 1st factor of the product is equal to twenty four. The 2nd factor of the product is equal to a. The 3rd factor of the product is equal to a power. The base is c. The exponent is three. The 4th factor of the product is x. The 7th term of the sum is equal to a negative power. The base is d. The exponent is three. The 8th term of the sum is equal to a product that contains 3 factors. The 1st factor of the product is equal to six. The 2nd factor of the product is equal to c. The 3rd factor of the product is a power. The base is d. The exponent is two. The 9th term of the sum is a negative product containing 3 factors. The 1st factor of the product is equal to twelve. The 2nd factor of the product is a power. The base is c. The exponent is two. The 3rd factor of the product is equal to d. The ten term of the sum is equal to a product that contains 2 factors. The 1st factor of the product is equal to eight. The 2nd factor of the product is equal to a power. The base is c. The exponent is three.
  2. eight times a to the power three times c to the power of three times x raised to the power three plus negative twelve times a raised to the power of two times c raised to the power of two times d times x to the power two plus twenty four times a exponentiated by two multiplied by c to the power three times x to the power of two plus six multiplied by a multiplied by c times d to the power two multiplied by x plus negative twenty four times a multiplied by c exponentiated by two multiplied by d multiplied by x plus twenty four times a times c to the power of three multiplied by x plus negative d raised to the power of three plus six times c multiplied by d to the power of two plus negative twelve multiplied by c to the power of two multiplied by d plus eight multiplied by c to the power three;