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Use Pascal's Triangle to expand 
(x+z)^(4). Express your answer in simplest form.
Answer:

Use Pascal's Triangle to expand (x+z)4 (x+z)^{4} . Express your answer in simplest form.\newlineAnswer:

Full solution

Q. Use Pascal's Triangle to expand (x+z)4 (x+z)^{4} . Express your answer in simplest form.\newlineAnswer:
  1. Identify Pascal's Triangle Row: Identify the 4th4^{\text{th}} row of Pascal's Triangle to determine the coefficients for the expansion of (x+z)4(x+z)^{4}. The 4th4^{\text{th}} row of Pascal's Triangle (starting with row 00) is 1,4,6,4,11, 4, 6, 4, 1.
  2. Write Expansion Terms: Write out the terms of the expansion using the coefficients from Pascal's Triangle.\newlineThe expansion will have the form: 1(x4)+4(x3z)+6(x2z2)+4(xz3)+1(z4)1*(x^4) + 4*(x^3*z) + 6*(x^2*z^2) + 4*(x*z^3) + 1*(z^4).
  3. Simplify Expansion Terms: Simplify the terms of the expansion.\newlineThe simplified form is: x4+4x3z+6x2z2+4xz3+z4x^4 + 4x^3z + 6x^2z^2 + 4xz^3 + z^4.

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