Bài 73 trang 32 sgk toán 8 tập 1

Tính nhanh: 73. 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.