# How do you multiply (x + y)^6?

Sep 11, 2015

${x}^{6} + 6 {x}^{5} y + 15 {x}^{4} {y}^{2} + 20 {x}^{3} {y}^{3} + 15 {x}^{2} {y}^{4} + 6 x {y}^{5} + {y}^{6}$
${\left(x + y\right)}^{6} = {x}^{6} + \frac{6}{1} {x}^{5} y + \frac{6 \cdot 5}{2 \cdot 1} {x}^{4} {y}^{2} + \frac{6 \cdot 5 \cdot 4}{3 \cdot 2 \cdot 1} {x}^{3} {y}^{3} + \frac{6 \cdot 5 \cdot 4 \cdot 3}{4 \cdot 3 \cdot 2 \cdot 1} {x}^{2} {y}^{4} + \frac{6 \cdot 5 \cdot 4 \cdot 3 \cdot 2}{5 \cdot 4 \cdot 3 \cdot 2 \cdot 1} x {y}^{5} + \frac{6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1} {y}^{6}$
= ${x}^{6} + 6 {x}^{5} y + 15 {x}^{4} {y}^{2} + 20 {x}^{3} {y}^{3} + 15 {x}^{2} {y}^{4} + 6 x {y}^{5} + {y}^{6}$