Chọn câu sai A. x 2 + 4x – y 2 + 4 = (x – y + 2)(x + y+ 2) B. (2x 2 – y) 2 – 64y 2 = (2x 2 – 9y)(2x 2 + 7y) C. -x 3 + 6x 2 y – 12xy 2 + 8y 3 = (2y – x) 3 D. x 8 – y 8 = (x 4 ) 2 – (y 4 ) 2 = (x 4 + y 4 )(x 2 + y 2 )(x + y)

Giải thích

Lời giải +) x 2 + 4x – y 2 + 4 = (x 2 + 4x + 4) – y 2 = (x 2 + 2.2.x +2 2 ) – y 2 = (x + 2) 2 – y 2 = (x + 2 + y)(x + 2 – y) +) (2x 2 – y) 2 – 64y 2 = (2x 2 – y) 2 – (8y) 2 = (2x 2 – y – 8y)(2x 2 – y + 8y) = (2x 2 – 9y)(2x 2 +7y) +) -x 3 + 6x 2 y – 12xy 2 + 8y 3 = (-x) 3 + 3.x 2 .2y + 3(-x)(2y) 3 + (2y) 3 = (-x + 2y) 3 = (2y – x) 3 +) x 8 – y 8 = (x 4 ) 2 – (y 4 ) 2 = (x 4 + y 4 )(x 4 – y 4 ) = (x 4 + y 4 )(x 2 + y 2 )(x 2 – y 2 ) = (x 4 + y 4 )(x 2 + y 2 )(x + y)(x – y) Nên A, B, C đúng, D sai Đáp án cần chọn là: D. x 8 – y 8 = (x 4 ) 2 – (y 4 ) 2 = (x 4 + y 4 )(x 2 + y 2 )(x + y)