Use Pascal's Triangle to expand (5y^(2)+x^(2))^(3). Express your answer in simplest form. Answer:

Question

Use Pascal's Triangle to expand  (5y^(2)+x^(2))^(3). Express your answer in simplest form. Answer:

Bytelearn · Accepted Answer

Identify Row: Identify the row of Pascal's Triangle that corresponds to the exponent of the binomial expansion. Since we are expanding (5y^(2)+x^(2))^(3), we need the fourth row of Pascal's Triangle, which corresponds to the coefficients for a cubic expansion. The fourth row of Pascal's Triangle is 1, 3, 3, 1.Write Terms: Write out each term of the expansion using the binomial theorem and the coefficients from Pascal's Triangle. The binomial theorem tells us that (a+b)^n = Σ (n choose k) * a^(n-k) * b^k, where Σ denotes the sum over k from 0 to n. For (5y^(2)+x^(2))^(3), we have: 1*(5y^(2))^3*(x^(2))^0 + 3*(5y^(2))^2*(x^(2))^1 + 3*(5y^(2))^1*(x^(2))^2 + 1*(5y^(2))^0*(x^(2))^3Calculate Terms: Calculate each term of the expansion. Now we will calculate each term: 1*(5y^(2))^3*(x^(2))^0 = 1*(125y^(6))*(1) = 125y^(6) 3*(5y^(2))^2*(x^(2))^1 = 3*(25y^(4))*(x^(2)) = 75y^(4)x^(2) 3*(5y^(2))^1*(x^(2))^2 = 3*(5y^(2))*(x^(4)) = 15y^(2)x^(4) 1*(5y^(2))^0*(x^(2))^3 = 1*(1)*(x^(6)) = x^(6)Combine for Final Form: Combine all the terms to write the final expanded form. The final expanded form of (5y^(2)+x^(2))^(3) is: 125y^(6) + 75y^(4)x^(2) + 15y^(2)x^(4) + x^(6)

Use Pascal's Triangle to expand $\left(5 y^{2}+x^{2}\right)^{3}$ . Express your answer in simplest form. $\newline$ Answer:

Full solution

More problems from Pascal's triangle and the Binomial Theorem

Related topics

Use Pascal's Triangle to expand (5y2+x2)3 \left(5 y^{2}+x^{2}\right)^{3} (5y2+x2)3. Express your answer in simplest form.\newlineAnswer:

Use Pascal's Triangle to expand $\left(5 y^{2}+x^{2}\right)^{3}$ . Express your answer in simplest form. $\newline$ Answer: