Toán Lớp 8: Rút gọn các biểu thức sau: a) 2x(2x − 1)2 − 3x(x + 3)(x − 3) − 4x(x + 1)2 b) (a − b + c) 2 − (b − c) 2 + 2ab − 2ac. c) (3x + 1)2 − 2(3x

Question

Toán Lớp 8:  Rút gọn các biểu thức sau: a) 2x(2x − 1)2 − 3x(x + 3)(x − 3) − 4x(x + 1)2 b) (a − b + c) 2 − (b − c) 2 + 2ab − 2ac. c) (3x + 1)2 − 2(3x + 1)(3x + 5) + (3x + 5)2. d) 4(32 + 1)(34 + 1)(38 + 1)(316 + 1)(332 + 1).

daithanh · Answer

a)2x(2x-1)&sup2;-3x(x+3)(x-3)-4x(x+1)&sup2;   =2x(4x&sup2;-4x+1)-3x(x&sup2;-9)-4x(x&sup2;+2x+1)   =8x&sup3;-8x&sup2;+2x-3x&sup3;+27x-4x&sup3;-8x&sup2;-4x   =(8x&sup3;-3x&sup3;-4x&sup3;)+(-8x&sup2;-8x&sup2;)+(2x+27x-4x)   =x&sup3;-16x&sup2;+25x   b)(a-b+c)&sup2;-(b-c)&sup2;+2ab-2ac   =(a-b+c+b-c)(a-b+c-b+c)+2ab-2ac   =a(a-2b+2c)+2ab-ac   =a&sup2;-2ab+2ac+2ab-2ac   =a&sup2;+(-2ab+2ab)+(2ac-2ac)   =a&sup2;   c)(3x+1)&sup2;-2(3x+1)(3x+5)+(3x+5)&sup2;   =[(3x+1)-(3x+5)]&sup2;   =(3x+1-3x-5)&sup2;   =(-4)&sup2;   =16   d)4(3&sup2;+1)(3^4+1)(3^8+1)(3^16+1)(3^32+1)   =[8(3&sup2;+1)(3^4+1)(3^8+1)(3^16+1)(3^32+1)]/2   =[(3^2-1)(3&sup2;+1)(3^4+1)(3^8+1)(3^16+1)(3^32+1)]/2   =[[(3^2)^2-1^2](3^4+1)(3^8+1)(3^16+1)(3^32+1)]/2   =[(3^4-1)(3^4+1)(3^8+1)(3^16+1)(3^32+1)]/2   =[[(3^4)^2-1^2](3^8+1)(3^16+1)(3^32+1)]/2   =[(3^8-1)(3^8+1)(3^16+1)(3^32+1)]/2   =[[(3^8)^2-1^2](3^16+1)(3^32+1)]/2   =[(3^16-1)(3^16+1)(3^32+1)]/2   =[[(3^16)^2-1^2](3^32+1)]/2   =[(3^32-1)(3^32+1)]/2   =[(3^32)^2-1^2]/2   =(3^64-1)/2

huenthanh97 · Answer

Giải đáp+Lời giải và giải thích chi tiết:     a)2x(2x-1)^2-3x(x+3)(x-3)-4x(x+1)^2   =2x(4x^2-4x+1)-3x(x^2-9)-4x(x^2+2x+1)   =8x^3-8x^2+2x-3x^3+27x-4x^3-8x^2-4x   =x^3-16x^2+25x   b)(a-b+c)^2-(b-c)^2+2ab-2ac   =a^2+b^2+c^2-2ab-2bc+2ac-b^2+2bc-c^2+2ab-2ac   =a^2   c)(3x+1)^2-2(3x+1)(3x+5)+(3x+5)^2   =(3x+1-3x-5)^2   =(-4)^2   =16   d)4(3^2+1)(3^4+1)(3^8+1)(3^16+1)(3^32+1)   =(8(3^2+1)(3^4+1)(3^8+1)(3^16+1)(3^32+1))/2   =((3^2-1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)(3^32+1))/2   =((3^4-1)(3^4+1)(3^8+1)(3^16+1)(3^32+1))/2   =((3^8-1)(3^8+1)(3^16+1)(3^32+1))/2   =((3^16-1)(3^16+1)(3^32+1))/2   =((3^32-1)(3^32+1))/2   =(3^64-1)/2