Question

Answer 1

1) 

a) (x + 2)² - (x² - 6x + 9)

= (x + 2)² - (x - 3)²

= [(x + 2) + (x - 3)][(x + 2) - (x - 3)]

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

= 2x - 1).5

= 5(2x - 1)

b) x⁴ - 2x³y + x²y² - 9x²

= x²(x² - 2xy + y² - 9)

= x²[(x² - 2xy + y²) - 3²]

= x²[(x - 1)² - 3²]

= x²(x - 1 - 3)(x - 1 + 3)

= x²(x - 4)(x + 2)

c) x² - 4x + 4 - y²

= (x² - 4x + 4) - y²

= (x - 2)² - y²

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

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

d) x² - 6xy + 9y² + xz - 3yz

= (x² - 6xy + 9y²) + (xz - 3yz)

= (x - 3y)² + z(x - 3y)

= (x - 3y)(x - 3y + z)

e) Sửa đề:

x³ - 3x² + 3x - 1 - y³

= (x³ - 3x² + 3x - 1) - y³

= (x - 1)³ - y³

= (x - 1 - y)[(x - 1)² + (x - 1)y + y²]

= (x - y - 1)(x² - 2x + 1 + xy - y + y²)

g) x² - 3x - 4

= x² - 4x + x - 4

= (x² - 4x) + (x - 4)

= x(x - 4) + (x - 4)

= (x - 4)(x + 1)

Answer 2

2)

a) (27x⁵y⁴ - 3x⁴y³ + 18x³y²) : 3x³y²

= 27x⁵y⁴ : 3x³y² - 3x⁴y³ : 3x³y² + 18x³y² : 3x³y²

= 9x²y² - xy + 6

b) (-5x⁸y⁴ + 24x⁶y⁵ + 7x⁵y³) : (-7x⁵y²)

= [-5x⁸y⁴ : (-7x⁵y²)] - 24x⁶y⁵ : 7x⁵y² - 7x⁵y³ : 7x⁵y²

= 5/7 x³y² - 24/7 xy³ - y

c) 4x²y(3x - 2y²) - 3x²y(4x - y²)

= 12x³y - 8x²y³ - 12x³y + 3x²y³

= (2x³y - 12x³y) + (-8x²y³ + 3x²y³)

= -5x²y³

d) (x + y)² + (x - y)² - 2(x² - 3) + 2y(x - y)

= x² + 2xy + y² + x² - 2xy + y² - 2x² + 6 + 2xy - 2y²

= (x² + x² - 2x²) + (2xy - 2xy + 2xy) + (y² + y² - 2y²) + 6

= 2xy + 6