1) This problems has two parts, Part A and Part B. Part A: What is the summation notation of LaTeX: \left(x+y\right)^5 ( x + y ) 5 ? Part B: Expand LaTeX: \left(x+y\right)^5 ( x + y ) 5 using the Binomial Theorem. A: LaTeX: \sum\begin{matrix}5\\k=0\end{matrix }\:\binom{5}{k}x^{5-k}y^k=\binom{5} {0}x^{5-0}y^0+\binom{5}{1}x^{5-1}y^ 1+\binom{5}{2}x^{5-2}y^2+\binom{5}{ 3}x^{5-3}y^3+\binom{5}{4}x^{5-4}y^4 +\binom{5}{5}x^{5-5}y^5 A: LaTeX: \sum\begin{matrix}5\\k=1\end{matrix }\:\binom{5}{k}x^{5-k}y^k=\binom{5} {1}x^{5-1}y^1+\binom{5}{2}x^{5-2}y^ 2+\binom{5}{3}x^{5-3}y^3+\binom{5}{ 4}x^{5-4}y^4+\binom{5}{5}x^{5-5}y^5 A: LaTeX: \sum\begin{matrix}5\\k=0\end{matrix }\:\binom{5}{k}x^{5-k}y^k=\binom{5} {0}x^0y^{5-0}+\binom{5}{1}x^1y^{5-1 }+\binom{5}{2}x^2y^{5-2}+\binom{5}{ 3}x^3y^{5-3}+\binom{5}{4}x^4y^{5-4} +\binom{5}{5}x^5y^{5-5} B: LaTeX: x^5-5x^4y-10x^3y^2+10x^2y^3-5xy^4-y ^5 B: LaTeX: x^5+5x^4y+10x^3y^2+10x^2y^3+5xy^4+y ^5 B: LaTeX: x^5+5x^4y+10x^3y^2+15x^2y^3+5xy^4+y ^5