Answer Key 6.9

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

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

\(\text{Equation: }\)

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