The formula for the sum of a series of cubes is as follows:
13 + 23 + 33 + ... + n3 = [n2*(n+1)2]/4
You may notice that this is the same as the square of the sum 1 + 2 + 3 + ... + n.
153 cubed is 3581577. And the sum of one number is itself.
a3 + b3
X3 + a3 = (X + a)(X2- aX + a2)Just a formula so that when you see an expression of any value that is additive cubes ( on the left ) then you can factor it. Works in any direction and some expressions can be manipulated into this form for factoring.
The formula ( a^3 + b^3 ) can be factored using the identity ( a^3 + b^3 = (a + b)(a^2 - ab + b^2) ). This means that the sum of the cubes of two numbers can be expressed as the product of the sum of those numbers and a quadratic expression. The quadratic part, ( a^2 - ab + b^2 ), captures the relationship between the two cubes and is useful for simplifying calculations or solving equations involving cubes. This factorization is particularly helpful in algebraic manipulations and solving polynomial equations.
The sum of the first five prime numbers is 28. The sum of the cubes of the first three prime numbers is 160. The average of 28 and 160 is 94.
The sum of two cubes can be factored as below.a3 + b3 = (a + b)(a2 - ab + b2)
There's a formula for the sum of cubes. (3x + 4)(9x^2 - 12x + 16)
The sum of the cubes of the first 100 whole numbers is 25,502,500.
(xy + 7)(x^2y^2 - 7xy + 49)
There is a formula for the sum of cubes. In this case, it's (b + 1)(b^2 - b + 1)
no
The sum of their squares is 10.
1
153 cubed is 3581577. And the sum of one number is itself.
a3 + b3
X3 + a3 = (X + a)(X2- aX + a2)Just a formula so that when you see an expression of any value that is additive cubes ( on the left ) then you can factor it. Works in any direction and some expressions can be manipulated into this form for factoring.
That means that you calculate the cubes of two numbers, and then either add or subtract them.