Question

Expand this equation (x+delta x) ^3

Answer 1

To expand the equation (x+δx)^3, use the binomial expansion formula and evaluate the binomial coefficients.

Step-by-step explanation:

To expand the equation (x+δx)^3, we can use the binomial expansion formula. The formula states that (a+b)^n = C(n,0)a^n * b^0 + C(n,1)a^(n-1) * b^1 + C(n,2)a^(n-2) * b^2 + ... + C(n,n)a^0 * b^n, where C(n,k) is the binomial coefficient.

Applying this formula to (x+δx)^3, we have:

(x+δx)^3 = C(3,0)x^3 * (δx)^0 + C(3,1)x^2 * (δx)^1 + C(3,2)x^1 * (δx)^2 + C(3,3)x^0 * (δx)^3

Now we can simplify each term by evaluating the binomial coefficients:

(x+δx)^3 = x^3 + 3x^2 * δx + 3x * (δx)^2 + (δx)^3

Answer 2

x^3 + 3 x^2 delta-X + 3 x delta-X^2 + (delta-X)^3
(x + delta-X)^3 = (x + delta-X)^2 (x + delta-X)
= (x^2 + 2 x delta-X + delta-X^2) (x + delta-X)
= (x^2 + 2x delta-X + delta-X^2) * x + (x^2 + 2x delta-X + delta-X^2) * delta-X
= x^3 + 2x^2 delta-X + x delta-X^2 + x^2 delta-X + 2x delta-X^2 + delta-X^3
= x^3 + 3x^2 delta-X + 3 x delta-X^2 + delta-X^3
(nC0) a^n + (nC1) a^(n-1) b + (nC2) a^(n-2) b^2 + ... (nCn-1) a b^(n-1) + (nCn) b^n