Expand Using Pascal's Triangle (2x+1)^4

Problem

(2*x+1)4

Solution

1. Identify the row of Pascal's Triangle corresponding to the power n=4 The coefficients for the expansion are 1, 4, 6, 4, 1$.

2. Set up the binomial expansion formula for (a+b)n where a=2*x and b=1

3. Apply the formula by multiplying each coefficient from Pascal's Triangle by descending powers of a and ascending powers of b

(2*x+1)4=1*(2*x)4*(1)0+4*(2*x)3*(1)1+6*(2*x)2*(1)2+4*(2*x)1*(1)3+1*(2*x)0*(1)4

4. Evaluate the powers of each term.

(2*x+1)4=1*(16*x4)*(1)+4*(8*x3)*(1)+6*(4*x2)*(1)+4*(2*x)*(1)+1*(1)*(1)

5. Simplify the expression by performing the final multiplications.

(2*x+1)4=16*x4+32*x3+24*x2+8*x+1

Final Answer

(2*x+1)4=16*x4+32*x3+24*x2+8*x+1

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