Question

Calcule os produtos:

a) 3x . ( 5x 2 + 2x – 4)
b) 5x 2 . (5x – 1)
c) -3 (2x 2 + x - 5)
d) (3x – 1) . (5x 2 - 3)
e) (2x 2 + x -2) (5x – 3)

Answer 1

Explicação passo-a-passo:

a) 3x . ( 5x 2 + 2x – 4)

$3x\left(5x\cdot \:2+2x-4\right)=\\\\\mathrm{Multiplicar\:os\:numeros:}\:5\cdot \:2=10\\=3x\left(10x+2x-4\right)\\\\\mathrm{Somar\:elementos\:similares:}\:10x+2x=12x\\=3x\left(12x-4\right)\\\\\mathrm{Colocar\:os\:parenteses\:utilizando}:\quad \:a\left(b-c\right)=ab-ac\\a=3x,\:b=12x,\:c=4\\\\=3x\cdot \:12x-3x\cdot \:4\\=3\cdot \:12xx-3\cdot \:4x\\=36x^2-12x$

b)5x 2 . (5x – 1)

$5x\:2\:.\:\left(5x\:-\:1\right)=\\\\\mathrm{Multiplicar\:os\:numeros:}\:5\cdot \:2=10\\=10x\left(5x-1\right)\\\\\mathrm{Colocar\:os\:parenteses\:utilizando}:\quad \:a\left(b-c\right)=ab-ac\\a=10x,\:b=5x,\:c=1\\\\=10x\cdot \:5x-10x\cdot \:1\\=10\cdot \:5xx-10\cdot \:1\cdot \:x\\=50x^2-10x$

c) -3 (2x 2 + x - 5)

$-3 (2x 2 + x - 5)=\\\\\mathrm{Multiplicar\:os\:numeros:}\:2\cdot \:2=4\\=-3\left(4x+x-5\right)\\\\\mathrm{Somar\:elementos\:similares:}\:4x+x=5x\\=-3\left(5x-5\right)\\\\\mathrm{Colocar\:os\:parenteses\:utilizando}:\quad \:a\left(b-c\right)=ab-aca\\\\=-3,\:b=5x,\:c=5\\\\=-3\cdot \:5x-\left(-3\right)\cdot \:5\\\\\\\mathrm{Aplicar\:as\:regras\:dos\:sinais}\\-\left(-a\right)=a\\=-3\cdot \:5x+3\cdot \:5\\\\\mathrm{Multiplicar\:os\:numeros:}\:3\cdot \:5=15\\=-15x+15$

d) (3x – 1) . (5x 2 - 3)

$(3x – 1) . (5x 2 - 3)=\\\\\mathrm{Multiplicar\:os\:numeros:}\:5\cdot \:2=10\\=\left(3x-1\right)\left(10x-3\right)\\\\\mathrm{Aplique\:o\:metodo\:FOIL}:\quad \left(a+b\right)\left(c+d\right)=ac+ad+bc+bd\\a=3x,\:b=-1,\:c=10x,\:d=-3\\\\=3x\cdot \:10x+3x\left(-3\right)+\left(-1\right)\cdot \:10x+\left(-1\right)\left(-3\right)\\\\\mathrm{Aplicar\:as\:regras\:dos\:sinais}: +\left(-a\right)=-a,\:\:\left(-a\right)\left(-b\right)=ab\\\\=3\cdot \:10xx-3\cdot \:3x-1\cdot \:10x+1\cdot \:3\\=30x^2-19x+3$

e) (2x 2 + x -2) (5x – 3)

$\left(2x\:2\:+\:x\:-2\right)\:\left(5x\:-\:3\right)=\\\\\mathrm{Multiplicar\:os\:numeros:}\:2\cdot \:2=4\\=\left(4x+x-2\right)\left(5x-3\right)\\\\\mathrm{Somar\:elementos\:similares:}\:4x+x=5x\\=\left(5x-2\right)\left(5x-3\right)\\\\\mathrm{Aplique\:o\:metodo\:FOIL}:\quad \left(a+b\right)\left(c+d\right)=ac+ad+bc+bd\\a=5x,\:b=-2,\:c=5x,\:d=-3\\\\=5x\cdot \:5x+5x\left(-3\right)+\left(-2\right)\cdot \:5x+\left(-2\right)\left(-3\right)$

$\mathrm{Aplicar\:as\:regras\:dos\:sinais} : +\left(-a\right)=-a,\:\:\left(-a\right)\left(-b\right)=ab\\=5\cdot \:5xx-5\cdot \:3x-2\cdot \:5x+2\cdot \:3\\=25x^2-25x+6$