Giúp em bài 24 vs ạ em đang cần ạ

Ans:

 a)

$(2x + y^2)^3$

$= (2x)^3 + 3 \cdot (2x)^2 \cdot y^2 + 3 \cdot 2x \cdot (y^2)^2 + (y^2)^3$

$= 8x^3 + 12x^2y^2 + 6xy^4 + y^6$

b)

$\left(\dfrac{1}{2}x^2 + \dfrac{1}{3}y\right)^3$

$= \left(\dfrac{1}{2}x^2\right)^3 + 3 \cdot \left(\dfrac{1}{2}x^2\right)^2 \cdot \left(\dfrac{1}{3}y\right) + 3 \cdot \left(\dfrac{1}{2}x^2\right) \cdot \left(\dfrac{1}{3}y\right)^2 + \left(\dfrac{1}{3}y\right)^3$

$= \dfrac{1}{8}x^6 + \dfrac{1}{4}x^4y + \dfrac{1}{6}x^2y^2 + \dfrac{1}{27}y^3$

c)

$(3x^2 - 2y)^3$

$= (3x^2)^3 - 3 \cdot (3x^2)^2 \cdot (2y) + 3 \cdot (3x^2) \cdot (2y)^2 - (2y)^3$

$= 27x^6 - 54x^4y + 36x^2y^2 - 8y^3$

d)

$\left(\dfrac{2}{3}x^2 - \dfrac{1}{2}y\right)^3$

$= \left(\dfrac{2}{3}x^2\right)^3 - 3 \cdot \left(\dfrac{2}{3}x^2\right)^2 \cdot \left(\dfrac{1}{2}y\right) + 3 \cdot \left(\dfrac{2}{3}x^2\right) \cdot \left(\dfrac{1}{2}y\right)^2 - \left(\dfrac{1}{2}y\right)^3$

$= \dfrac{8}{27}x^6 - \dfrac{2}{3}x^4y + \dfrac{1}{2}x^2y^2 - \dfrac{1}{8}y^3$

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