Rút gọn biểu thức (2x + y)^3 – 8x^3 – y^3.
Giải thích
(2x + y)3 – 8x3 – y3
= (2x)3 + 3 . (2x)2 . y + 3 . 2x . y2 + y3 – 8x3 – y3
= 8x3 + 12x2y + 6xy2 + y3 – 8x3 – y3
= (8x3 – 8x3) + 12x2y + 6xy2 + (y3 – y3)
= 12x2y + 6xy2.
(2x + y)3 – 8x3 – y3
= (2x)3 + 3 . (2x)2 . y + 3 . 2x . y2 + y3 – 8x3 – y3
= 8x3 + 12x2y + 6xy2 + y3 – 8x3 – y3
= (8x3 – 8x3) + 12x2y + 6xy2 + (y3 – y3)
= 12x2y + 6xy2.