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*x4*h0+4*x3*h1+6*x2*h2+4*x1*h3+1*x0*h4

5. Simplify the terms by removing exponents of 1 and terms with h0 or x0

x4+4*x3*h+6*x2*h2+4*x*h3+h4

Final Answer

(x+h)4=x4+4*x3*h+6*x2*h2+4*x*h3+h4

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