Question

Tính nhanh :

a) \(\left(4x^2-9y^2\right):\left(2x-3y\right)\)

b) \(\left(27x^3-1\right):\left(3x-1\right)\)

c) \(\left(8x^3+1\right):\left(4x^2-2x+1\right)\)

d) \(\left(x^2-3x+xy-3y\right):\left(x+y\right)\)

Answer 1

a) (4x² – 9y²) : (2x – 3y) = [(2x)² – (3y)²] : (2x – 3y) = 2x + 3y;

b) (27x³ – 1) : (3x – 1) = [(3x)³ – 1] : (3x – 1) = (3x)² + 3x + 1 = 9x² + 3x + 1

c) (8x³ + 1) : (4x² – 2x + 1) = [(2x)³ + 1] : (4x² – 2x + 1)

= (2x + 1)[(2x)² – 2x + 1] : (4x² – 2x + 1)

= (2x + 1)(4x² – 2x + 1) : (4x² – 2x + 1) = 2x + 1

d) (x² – 3x + xy -3y) : (x + y)

= [(x² + xy) – (3x + 3y)] : (x + y)

= [x(x + y) – 3(x + y)] : (x + y)

= (x + y)(x – 3) : (x + y)

= x – 3.

Answer 2

Tính nhanh:

a) (4x² – 9y²) : (2x – 3y); b) (27x³ – 1) : (3x – 1);

c) (8x³ + 1) : (4x² – 2x + 1); d) (x² – 3x + xy -3y) : (x + y)

Bài giải:

a) (4x² – 9y²) : (2x – 3y) = [(2x)² – (3y)²] : (2x – 3y) = 2x + 3y;

b) (27x³ – 1) : (3x – 1) = [(3x)³ – 1] : (3x – 1) = (3x)² + 3x + 1 = 9x² + 3x + 1

c) (8x³ + 1) : (4x² – 2x + 1) = [(2x)³ + 1] : (4x² – 2x + 1)

= (2x + 1)[(2x)² – 2x + 1] : (4x² – 2x + 1)

= (2x + 1)(4x² – 2x + 1) : (4x² – 2x + 1) = 2x + 1

d) (x² – 3x + xy -3y) : (x + y)

= [(x² + xy) – (3x + 3y)] : (x + y)

= [x(x + y) – 3(x + y)] : (x + y)

= (x + y)(x – 3) : (x + y)

= x – 3.