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The coefficient of x¹₂ in the expansion of (1 + x)⁶(1 + x²)⁷ is

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1. **Series Expansion**:
   - $(1+x)^6 = \sum_{r=0}^6 \binom{6}{r} x^r$
   - $(1+x^2)^7 = \sum_{s=0}^7 \binom{7}{s} x^{2s}$
2. **Compound Term**: We need $x^k$ where $k = r + 2s = 12$.
3. **Valid Pairs** ($r, s$):
   - $s=6 \implies r=0: \binom{6}{0} \binom{7}{6} = 1 	imes 7 = 7$
   - $s=5 \implies r=2: \binom{6}{2} \binom{7}{5} = 15 	imes 21 = 315$
   - $s=4 \implies r=4: \binom{6}{4} \binom{7}{4} = 15 	imes 35 = 525$
   - $s=3 \implies r=6: \binom{6}{6} \binom{7}{3} = 1 	imes 35 = 35$
4. **Summation**: Total $= 7 + 315 + 525 + 35 = 882$.

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