Question

2. Determine o 3º termo no desenvolvimento de: * 1 ponto Imagem sem legenda a) 69x² b) 16x² c) 96x² d) 96

Answer 1

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$\Large\boxed{\sf{\underline{Termo~geral~do~bin\hat omio~de~\frak {Newton}}}}\\\boxed{\boxed{\boxed{\boxed{\sf T_{p+1}=\binom{n}{p}a^{n-p\cdo}\cdot b^p}}}}$

$\sf(2x+2)^4\\\sf a=2x~b=2~n=4\\\sf p+1=3\implies p=3-1=2\\\sf T_{2+1}=\binom{4}{2}(2x)^{4-2}\cdot 2^2\\\sf T_3=\dfrac{4\cdot3}{2\cdot1}(2x)^2\cdot4\\\sf T_{3}=6\cdot4x^2\cdot4\\\huge\boxed{\boxed{\boxed{\boxed{\sf T_3=96x^2}}}}$