Q. Use Pascal's Triangle to expand (x+z)4. Express your answer in simplest form.Answer:
Identify Pascal's Triangle Row: Identify the 4th row of Pascal's Triangle to determine the coefficients for the expansion of (x+z)4. The 4th row of Pascal's Triangle (starting with row 0) is 1,4,6,4,1.
Write Expansion Terms: Write out the terms of the expansion using the coefficients from Pascal's Triangle.The expansion will have the form: 1∗(x4)+4∗(x3∗z)+6∗(x2∗z2)+4∗(x∗z3)+1∗(z4).
Simplify Expansion Terms: Simplify the terms of the expansion.The simplified form is: x4+4x3z+6x2z2+4xz3+z4.
More problems from Pascal's triangle and the Binomial Theorem