Question

Desenvolva os produtos notáveis
A) (2x+y)²
B) (3x-2y)²
C) (3x²-4) (3x²+4)
???

Answer 1

Veja alguns dos produtos notáveis:

• (a + b)² <=> a² + 2ab + b²
• (a – b)² <=> a² – 2ab + b³
• (a – b).(a + b) <=> a ² – b²

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Assim, desenvolvendo:

Letra A)

$\begin{array}{l}\sf (2x+y)^2\\\\\sf (2x+y)^2=(2x)^2+2\cdot(2x)\cdot(y)+(y)^2\\\\\sf (2x+y)^2=\boldsymbol{\boxed{\sf4x^2+4xy+y^2}}\end{array}$

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Letra B)

$\begin{array}{l}\sf (3x-2y)^2\\\\\sf (3x-2y)^2=(3x)^2-2\cdot(3x)\cdot(2y)+(2y)^2\\\\\sf (3x-2y)^2=\boldsymbol{\boxed{\sf9x^2-12xy+4y^2}}\end{array}$

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Letra C)

$\begin{array}{l}\sf (3x^2-4)\cdot(3x^2+4) \\ \\ \sf (3x^2-4)\cdot(3x^2+4)=(3x^2)^2-(4)^2\\\\\!\sf (3x^2-4)\cdot(3x^2+4)=\boldsymbol{\boxed{ \sf9x^4-16}}\end{array}$

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Att. Nasgovaskov

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