Question

Substituindo a = 2, b = 1e c = 3 na expressão (a + b + 2c)2 + (3a + 2b + 2c)2 + 2abc, o valor encontrado é​

Answer 1

• Sem utilizar tais, como: a = 2, b = 1 e c = 3

$\left(a+b+2c\right)^2+\left(3a+2b+2c\right)^2+2abc\\\\=\left(a+b+2c\right)\left(a+b+2c\right)+\left(3a+2b+2c\right)^2+2abc\\\\=\left(a+b+2c\right)\left(a+b+2c\right)+\left(3a+2b+2c\right)\left(3a+2b+2c\right)+2abc\\\\=2ab+4ac+a^2+b^2+4bc+4c^2+\left(3a+2b+2c\right)\left(3a+2b+2c\right)+2abc\\\\=2ab+4ac+a^2+b^2+4bc+4c^2+12ab+12ac+9a^2+4b^2+8bc+4c^2+2abc\\\\=10a^2+14ab+16ac+2abc+5b^2+8c^2+12bc$

• Utilizando

$\left(2+1+23\right)^2+\left(32+21+23\right)^2+2213\\\\2+1+23\\\\=26\\\\=26^2+\left(32+21+23\right)^2+2213\\\\\\32+21+23\\\\=76\\\\=26^2+76^2+2213\\\\\\26^2=676\\\\=676+76^2+2213\\\\\\76^2=5776\\\\=676+5776+2213\\\\\\676+5776=6452\\\\6452+2213=8665\\\\=8665$

Answer 2

Resposta:

B) 289

Explicação passo a passo:

Substituindo os valores, temos:

(a + b + 2c)2 + (3a + 2b + 2c)3 + 2abc = (2 + 1 + 2 ∙ 3)2 + (3 ∙ 2 + 2 ∙ 1 + 2 ∙ 3)2 + 2 ∙ (2 ∙ 1 ∙ 3) =

(9)2 + (14)2 + 2(6) =

81 + 196 + 12 =

93 + 196 =

289

Espero ter ajudado! Bons estudos