Question

Faça em seu caderno a seguintes multiplicações:

a) 3ab(2a+4b)

b) -y(y²-2y)

c) -2x(x²-3x+2)

d) (2x+y)3x²

e) 3x²(2x³-x²+2x+1)

f) (a²+2ab+b²)3a²

Answer 1

$a)~~3ab(2a+4b) \to ~~ \boxed{6a^2b+12ab^2} \\\\\\ b)~~ -y(y^2-2y)\to~~ \boxed{-y^3+2y^2}\\\\\\ c)~~-2x(x^2-3x+2)\to ~~\boxed{ -2x^3+6x^2-4x}$



$d)~~ (2x+y)3x^2\to ~~ \boxed{6x^3+3x^2y}\\\\\\ e) ~~3 x^{2} (2x^3-x^2+2x+1)\to ~~ \boxed{6x^5-3x^4+6x^3+3x^2}\\\\\\ f) ~~(a^2+2ab+b^2)3a^2\to ~~ \boxed{3a^4+6a^3b+3a^2b^2}$

Answer 2

a)
= 3ab.(2a + 4b) 
= 3ab.2a + 3ab.4b
= 6a²b + 12ab²
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b)
= - y.(y² - 2y)
= - y.y² - y.(-2y)
= - y³ + 2y²
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c)
= - 2x.(x² - 3x + 2)
= - 2x.x² - 2x.(- 3x) - 2x.2
= - 2x³ + 6x² - 4x
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d)
= (2x + y).3x²
= 3x².(2x + y)
= 3x².2x + 3x².y
= 6x³ + 3x²y
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e)
= 3x².(2x³ - x² + 2x + 1)

= 3x².2x³ + 3x².(-x²) + 3x².2x + 3x².1

= 6x⁵ - 3x⁴ + 6x³ + 3x²

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f)
(a² + 2ab + b²).3a²

3a² . (a² + 2ab + b²)

3a².a² + 3a².2ab + 3a².b²

= 3a⁴ + 6a³b + 3a²b²