Question
En utilisant la formule du binôme de Newton, développer et réduire \((x+2)^5.\)
Solution
\((x+2)^5 =C_5^0 x^5×2^0+C_5^1 x^4 ×2^1+ C_5^2 x^3× 2^2+C_5^3 x^2× 2^3+C_5^4 x^1× 2^4+C_5^5 x^0× 2^5\)
\(=1x^5×1+5x^4×2+10x^3×2^2+10x^2×2^3+5x×2^4+1×2^5\)
donc \((x+2)^5 = x^5+10x^4+40x^3+80x^2+80x+32\)