Sách Toán 8 - bài 33 trang 16 - Tính: a) (2 + xy)2; b) (5 – 3x)2 Bài 33. Tính: a) (2 + xy)2 b) (5 – 3x)2 c) (5 – x2)(5 + x2) d) (5x – 1)3 e) (2x – y)(4x2 + 2xy + y2) f) (x + 3)(x2 – 3x + 9) Bài giải: a) (2 + xy)2 = 22 + 2 . 2 . xy + (xy)2 = 4 + 4xy + x2y2 b) (5 – 3x)2= 52 – 2 . 5 . 3x + (3x)2 = 25 – 30x + 9x2 c) (5 – x2)(5 + x2) = 52 – (x2)2 = 25 – x4 d) (5x – 1)3 = (5x)3 – 3 . (5x)2. 1 + 3 . 5x . 12 – 13 = 125x3 – 75x2 + 15x – 1 e) (2x – y)(4x2 + 2xy + y2) = (2x – y)[(2x)2 + 2x . y + y2] = (2x)3 – y3 = 8x3 – y3 f) (x + 3)(x2 – 3x + 9) = (x + 3)(x2 – 3x + 32) = x3 + 33 = x3 + 27.
Sách Toán 8 - bài 33 trang 16 - Tính: a) (2 + xy)2; b) (5 – 3x)2 Bài 33. Tính: a) (2 + xy)2 b) (5 – 3x)2 c) (5 – x2)(5 + x2) d) (5x – 1)3 e) (2x – y)(4x2 + 2xy + y2) f) (x + 3)(x2 – 3x + 9) Bài giải: a) (2 + xy)2 = 22 + 2 . 2 . xy + (xy)2 = 4 + 4xy + x2y2 b) (5 – 3x)2= 52 – 2 . 5 . 3x + (3x)2 = 25 – 30x + 9x2 c) (5 – x2)(5 + x2) = 52 – (x2)2 = 25 – x4 d) (5x – 1)3 = (5x)3 – 3 . (5x)2. 1 + 3 . 5x . 12 – 13 = 125x3 – 75x2 + 15x – 1 e) (2x – y)(4x2 + 2xy + y2) = (2x – y)[(2x)2 + 2x . y + y2] = (2x)3 – y3 = 8x3 – y3 f) (x + 3)(x2 – 3x + 9) = (x + 3)(x2 – 3x + 32) = x3 + 33 = x3 + 27.