Question

1)Rút gọn:

D=(-4x^3y^3+x^3y^3):2xy^2-xy(2y-xy)

2) 

a) 5x^3-7x^2+10x-14

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

c)81a^2-6bc-9b^2-c^2

d) 2x^2-12x+18+2xy-6y

e) x^2+4x-4y^2+8y

 

éc o éc!

Answer 1

1) D = (-4x³y³ + x³y³) : 2xy² - xy(2y - xy)

= 3x³y³ : 2xy² - xy.2y + xy.xy

= 3/2 x²y - 2xy² + x²y²

2) 

a) 5x³ - 7x² + 10x - 14)

= (5x³ - 7x²) + (10x - 14)

= x²(5x - 7) + 2(5x - 7)

= (5x - 7)(x² + 2)

b) (b - a)² + (a - b)(3a - 2b) - a² + b²

= (a - b)² + (a - b)(3a - 2b) - (a² - b²)

= (a - b)² + (a - b)(3a - 2b) - (a - b)(a + b)

= (a - b)(a - b + 3a - 2b - a - b)

= (a - b)(a - 4b)

c) 81a² - 6bc - 9b² - c²

= (9a)² - (9b² + 6bc + c²)

= (9a)² - (3b + 2c)²

= (9a - 3b - 2c)(9a + 3b +2c)

d) 2x² - 12x + 18 + 2xy - 6y

= 2(x² - 6x + 9 + xy - 3y)

= 2[(x² - 6x + 9) + (xy - 3y)]

= 2[(x - 3)² + y(x - 3)]

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

e) x² + 4x - 4y² + 8y

= x² + 4x + 4 - 4y² + 8y - 4

= (x² + 4x + 4) - (4y² - 8y + 4)

= (x + 2)² - (2y - 2)²

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

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