Question

(x+2)³ resolvido em binômio de newton

Answer 1

Boa tarde Memex!

Solução!

Binômio de Newton!

$(x +a)^{n}={n \choose 0}a^{0} . x^{n} +{n \choose 1}a. x^{n-1} +{n \choose 2}a^{2}. x^{n-2}........+ {n \choose n}a^{n}.x^{0}$

Lembrando que:

${n \choose p}={n \choose n-p}$


$(x+2)^{3}$


${3 \choose 0} x^{3}.2^{0}+ {3 \choose 1} x^{2} .2^{1} +{3 \choose 2} x^{1}.2^{2}+ {3\choose 3} x^{0}.2 ^{3}$


${3 \choose 3-0} x^{3}.2^{0}+ {3 \choose 3-1} x^{2} .2^{1} +{3 \choose3- 1} x^{1}.2^{2}+ {3\choose 3} x^{0}.2 ^{3}$


${3! \choose 3!} x^{3}.2^{0}+ {3! \choose 2!} x^{2} .2^{1} +{3! \choose2!} x^{1}.2^{2}+ {3!\choose 3!} x^{0}.2 ^{3!}$


$(x+2)^{2}= x^{3}+6 x^{2} +12x+8$


Boa tarde!
Bons estudos!