Question

Qual polinômio vou obter ao multiplicar (18x - 7) por (3x² - 12x + 8 ) ?

Answer 1

Resposta: 15X - 1

Explicação passo-a-passo:

(18X - 7) .  (3X² - 12X + 8)

(6X - 1) . (3X²)

(6X - 1) . (9X) = 54X - 1

Answer 2

$\sf \left(18x-7\right)\cdot\left(3x^2-12x+8\right)\\\\\\\\\\\large\boxed{\sf Aplique\:a\:regra\:dos\:produtos\:not\acute{a}veis }\\\\\\\\\\\sf 18x\cdot \:3x^2+18x\left(-12x\right)+18x\cdot \:8+\left(-7\right)\cdot\:3x^2+\left(-7\right)\left(-12x\right)+\left(-7\right)\cdot \:8\\\\\\\\\\\boxed{\sf Aplique\:as\:regras\:dos\:sinais\Rightarrow +\left(-a\right)=-a,\:\:\left(-a\right)\left(-b\right)=ab}\\\\\\\\\\\sf 18\cdot \:3x^2x-18\cdot\:12xx+18\cdot \:8x-7\cdot \:3x^2+7\cdot \:12x-7\cdot\:8$

$\sf =54x^3-216x^2+144x-21x^2+84x-56\\\\\\\\\sf \large{\boxed {\sf Agrupe\: os \:termos\:semelhantes}}\\\\\\\\\sf =54x^3-216x^2-21x^2+144x+84x-56\\\\\\\\\boxed{\sf Some\:os\:elementos\:similares\:-216x^2-21x^2=-237x^2}\\\\\\\\\sf =54x^3-237x^2+144x+84x-56\\\\\\\\\boxed{\sf Some\:os\:elementos\:similares\:144x+84x=228x}\\\\\\\\\boxed{\sf S_1=\{54x^3-237x^2+228x-56\}}$