Question

Đã trả lời bởi chuyên gia

Answer 1

(x + 3y)² - (2x - y)² - $\frac{6 x ⁵ y ² - 12 x ⁴ y ³ - \frac{2}{3} x ³ y ⁴}{- 3 x ³ y ²}$

(x + 3y)² = x² + 6xy + 9y²
(2x - y)² = 4x² - 4xy + y²

\frac{6 x ⁵ y ² - 12 x ⁴ y ³ - 2 / 3 x ³ y ⁴}{- 3 x ³ y ²}

= -2x² + 4xy + (2/9)y²

(x² + 6xy + 9y²) - (4x² - 4xy + y²) - (-2x² + 4xy + (2/9)y²)
= x² + 6xy + 9y² - 4x² + 4xy - y² + 2x² - 4xy - (2/9)y²
= -x² + 6xy + (80/9)y²

b) (a + b)³ + (a - b)³ - 2a³

(a ± b)³ = a³ ± 3a²b + 3ab² ± b³:

(a + b)³ = a³ + 3a²b + 3ab² + b³
(a - b)³ = a³ - 3a²b + 3ab² - b³

(a³ + 3a²b + 3ab² + b³) + (a³ - 3a²b + 3ab² - b³) - 2a³
= a³ + 3a²b + 3ab² + b³ + a³ - 3a²b + 3ab² - b³ - 2a³
= 6ab²

c) (x - 2y)² - 2(x - y)(x + 2y) - (x + 2y)²

(x - 2y)² = x² - 4xy + 4y²
2(x - y)(x + 2y) = 2(x² + xy - 2y²) = 2x² + 2xy - 4y²
(x + 2y)² = x² + 4xy + 4y²
(x² - 4xy + 4y²) - (2x² + 2xy - 4y²) - (x² + 4xy + 4y²)
= x² - 4xy + 4y² - 2x² - 2xy + 4y² - x² - 4xy - 4y²
= -2x² - 10xy + 4y²

Cho minh 5 sao nha

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Answer 2

(x + 3y)² - (2x - y)² - $\frac{6 x ⁵ y ² - 12 x ⁴ y ³ - \frac{2}{3} x ³ y ⁴}{- 3 x ³ y ²}$

(x + 3y)² = x² + 6xy + 9y²
(2x - y)² = 4x² - 4xy + y²

\frac{6 x ⁵ y ² - 12 x ⁴ y ³ - 2 / 3 x ³ y ⁴}{- 3 x ³ y ²}

= -2x² + 4xy + (2/9)y²

(x² + 6xy + 9y²) - (4x² - 4xy + y²) - (-2x² + 4xy + (2/9)y²)
= x² + 6xy + 9y² - 4x² + 4xy - y² + 2x² - 4xy - (2/9)y²
= -x² + 6xy + (80/9)y²

b) (a + b)³ + (a - b)³ - 2a³

(a ± b)³ = a³ ± 3a²b + 3ab² ± b³:

(a + b)³ = a³ + 3a²b + 3ab² + b³
(a - b)³ = a³ - 3a²b + 3ab² - b³

(a³ + 3a²b + 3ab² + b³) + (a³ - 3a²b + 3ab² - b³) - 2a³
= a³ + 3a²b + 3ab² + b³ + a³ - 3a²b + 3ab² - b³ - 2a³
= 6ab²

c) (x - 2y)² - 2(x - y)(x + 2y) - (x + 2y)²

(x - 2y)² = x² - 4xy + 4y²
2(x - y)(x + 2y) = 2(x² + xy - 2y²) = 2x² + 2xy - 4y²
(x + 2y)² = x² + 4xy + 4y²
(x² - 4xy + 4y²) - (2x² + 2xy - 4y²) - (x² + 4xy + 4y²)
= x² - 4xy + 4y² - 2x² - 2xy + 4y² - x² - 4xy - 4y²
= -2x² - 10xy + 4y²

Cho minh 5 sao nha

Answer 3

a) $(x+3y)^2-(2x-y)^2-(6x^5y^2-12x^4y^3-\frac{2}{3} x^3 y^4 ) : (-3x^3y^2)$

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

$= (x+3y + 2x-y)(x+3y - (2x-y))$

$= (3x + 2y)(-x + 4y)$

$= -3x^2 + 12xy - 2y^2$

$6x^5y^2 - 12x^4y^3 - \frac{2}{3}x^3y^4$

$= \frac{1}{3}x^3y^2(18x^2 - 36xy - 2xy^2)$

$\frac{-6x^5y^2 + 12x^4y^3 + \frac{2}{3}x^3y^4}{(-3x^3y^2)} = 2x - 4y - \frac{2}{3}y^2$

b) $(a+b)^3 + (a-b)^3 - 2a^3$

$(a+b)^3 + (a-b)^3$

$= 2a^3 + 6ab^2$

$2a^3 + 6ab^2 - 2a^3$

$= 6ab^2$

c) $(x-2y)^2 - 2(x-y)(x+2y) - (x+2y)^2$

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

$= -4xy - 4y^2$

$-2(x-y)(x+2y)$

$= -2(x^2 + 2xy - y^2 - 2y^2)$

$= -2x^2 - 4xy + 4y^2$

$-4xy - 4y^2 - 2x^2 - 4xy + 4y^2$

$= -2x^2 - 8xy$

Answer 4

Mong các bn rep tớ ạ

Answer 5

Mấy bn ơi tớ thấy ko đúng ý

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