Answer Key 6.9

Problem: Use Pascal’s triangle to expand the binomial $(a+b{)}^{12}.$

$\begin{array}{rc}\text{Row 10}& 1+10+44+120+210+252+210+120+44+10+1\\ \text{Row 11}& 1+11+54+164+330+462+462+330+164+54+11+1\\ \text{Row 12}& 1+12+65+218+494+792+924+792+494+218+65+12+1\end{array}$

$\text{Equation: }$

$\begin{array}{l}{a}^{12}+12a^{11}b+65a^{10}{b}^2+218a^9{b}^3+494a^8{b}^4+792a^7{b}^5+924a^6{b}^6+792a^5{b}^7+494a^4{b}^8+218a^3{b}^9+65a^2{b}^{10}+12a{b}^{11}+b^{12}\end{array}$