Toán Lớp 8: rút gọn : a. (x+2)^2-2(x^2-4)+(2-x)^2 b. (2a+3b)^2+(4a-6b)(2a+3b)+(2a-3b)^2 c. (a-b+c)+(c-b)^2+2(a-b+c)(b-c) d. 3(2^2+1)(2^4+1)(2^16+1

Question

Toán Lớp 8:  rút gọn : a. (x+2)^2-2(x^2-4)+(2-x)^2  b. (2a+3b)^2+(4a-6b)(2a+3b)+(2a-3b)^2 c. (a-b+c)+(c-b)^2+2(a-b+c)(b-c) d. 3(2^2+1)(2^4+1)(2^16+1)(2^32+1)-2^64

mocmien87 · Answer

Hướng dẫn trả lời:     a) (x + 2)^2 - 2.(x^2 - 4) + (2 - x)^2.   = (x + 2)^2 - 2.(x + 2).(x - 2) + (x - 2)^2.   = [(x + 2) - (x - 2)]^2.   = (x + 2 - x + 2)^2.   = 4^2.   = 16.   b) (2a + 3b)^2 + (4a - 6b).(2a + 3b) + (2a - 3b)^2.   = (2a + 3b)^2 + 2.(2a + 3b).(2a - 3b) + (2a - 3b)^2.   = [(2a + 3b) + (2a - 3b)]^2.   = (2a + 3b + 2a - 3b)^2.   = (4a)^2.   = 16a^2.   * C&acirc;u c bạn thiếu mũ 2, m&igrave;nh sửa lại đề nha.   c) (a - b + c)^2 + (c - b)^2 + 2.(a - b + c).(b - c).   = (a - b + c)^2 + 2.(a - b + c).(b - c) + (b - c)^2.   = [(a - b + c) + (b - c)]^2.   = (a - b + c + b - c)^2.   = a^2.   * Đề c&acirc;u d thiếu n&ecirc;n m&igrave;nh sửa lại nha.   d) 3.(2^2 + 1).(2^4 + 1).(2^8 + 1).(2^16 + 1).(2^32 + 1) - 2^64.   = (2^2 - 1).(2^2 + 1).(2^4 + 1).(2^8 + 1).(2^16 + 1).(2^32 + 1) - 2^64.   = [(2^2)^2 - 1^2].(2^4 + 1).(2^8 + 1).(2^16 + 1).(2^32 + 1) - 2^64.   = (2^4 - 1).(2^4 + 1).(2^8 + 1).(2^16 + 1).(2^32 + 1) - 2^64.   = [(2^4)^2 - 1^2].(2^8 + 1).(2^16 + 1).(2^32 + 1) - 2^64.   = (2^8 - 1).(2^8 + 1).(2^16 + 1).(2^32 + 1) - 2^64.   = [(2^8)^2 - 1^2].(2^16 + 1).(2^32 + 1) - 2^64.   = (2^16 - 1).(2^16 + 1).(2^32 + 1) - 2^64.   = [(2^16)^2 - 1^2].(2^32 + 1) - 2^64.   = (2^32 - 1).(2^32 + 1) - 2^64.   = [(2^32)^2 - 1^2] - 2^64.   = (2^64 - 1) - 2^64.   = 2^64 - 1 - 2^64.   = -1.