Question

Aplique a regra para desenvolver os produtos notáveis.

A) (3x + 5)²

B) (2x - 3y)²

C) (1/2x + 3)²

D) (2x/3 - 1/2)²

E) (x + 9) (x - 9)

F) ( 3x/4) (3x/4 - y)

Me ajuda gente!!! Eu necessito!

Answer 1

$a) \\ \\ (3x + 5)^2 \\ \\ (3x + 5)(3x + 5) \\ \\ 9x^2 + 15x + 15x + 25 \\ \\ => 9x^2 + 30x +25$

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$b) \\ \\ (2x - 3y)^2 \\ \\ (2x - 3y)(2x - 3y) \\ \\ 4x^2 - 6xy - 6xy + 9y^2 \\ \\ => 4x^2 - 12xy + 9y^2$

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$c) \\ \\ (\frac{1}{2}x + 3) ^2 \\ \\ \\ (\frac{1}{2}x + 3) (\frac{1}{2}x + 3) \\ \\ \\ \dfrac{1}{4}x^2 + \dfrac{3x}{2} + \dfrac{3x}{2} + 9 \\ \\ \\ => \dfrac{x^2 + 12x + 36}{4}$

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$d) \\ \\ (\dfrac{2x}{3} - \dfrac{1}{2})^2 \\ \\ \\ (\dfrac{2x}{3} - \dfrac{1}{2})(\dfrac{2x}{3} - \dfrac{1}{2}) \\ \\ \\ \dfrac{4x^2}{9} - \dfrac{2x}{6} - \dfrac{2x}{6} + \dfrac{1}{4} \\ \\ \\ => \dfrac{16x^2 - 24x + 9}{36}$

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$e \\ \\ (x + 9)(x - 9) \\ \\ \\ x^2 - 9x + 9x - 81 \\ \\ => x^2 - 81$

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$f) \\ \\ (\dfrac{3x}{4}) ( \dfrac{3x}{4} - y) \\ \\ \\ \dfrac{9x}{16} - \dfrac{3xy}{4} \\ \\ \\ => \dfrac{9x^2 - 12xy}{16y}$