Simplify (x+h)^4

Problem

(x+h)^4

Solution

1. Identify the expression as a binomial raised to the fourth power, which can be expanded using the Binomial Theorem.

2. Apply the formula for (a+b)^n where n=4 a=x and b=h

3. Determine the coefficients using the fourth row of Pascal's Triangle, which are $1, 4, 6, 4, 1$.

4. Write the expansion by decreasing the power of x and increasing the power of h for each term.

1*x^4*h^0+4*x^3*h^1+6*x^2*h^2+4*x^1*h^3+1*x^0*h^4

5. Simplify the terms by removing exponents of 1 and terms with h^0 or x^0

x^4+4*x^3*h+6*x^2*h^2+4*x*h^3+h^4

Final Answer

(x+h)^4=x^4+4*x^3*h+6*x^2*h^2+4*x*h^3+h^4

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