a)(a+b+c)2-(a+b)2-(a+c)2-(b+c)2
=a2+b2+c2+2ab+2bc+2ca-a2-2ab-b2-a2-2ac-c2-b2-2bc-c2
=-a2-b2-c2
=-(a2+b2+c2)
b)(a+b+c)2-(a-b+c)2+(a+b-c)2+(-a+b+c)2
=a2+2ab+b2+2bc+c2+2ac-a2-b2-c2+2ab+2bc-2ac+a2+b2+c2+2ab-2bc-2ac+a2+b2+c2-2ab-2ac+2bc
=2a2+2b2+2c2+4ab-4bc-4ac
Rút gọn :
a , ( a + b )^2 - ( b - a )^2
b , ( a + b )^3 - ( a - b ) - 2b^3
c , ( a + b + c )^2 - 2 ( a + b + c ) : ( b + c ) + ( b + c )^2
rút gọn biểu thức
a) (2x+3)^2-2(2x+3)(2x+5)+(2x+5)^2
b) (x^2+x+1)(x^2-x+1)(x^2-1)
c) (a+b-c)^2+(a-b+c)^2-2(b-c)^2
d) (a+b+c)^2+(a-b-c)^2+(b-c-a)^2+(c-a-b)^2
Rút gọn C=\(\dfrac{\text{ a^2b+b^2c+c^2a-ab^2-bc^2-ca^2}}{a^3\left(b^2-c^2\right)+b^3\left(c^2-a^2\right)+c^3\left(a^2-b^2\right)}\)
Bài 1: Cho a+b+c=0; rút gọn biểu thức A= a^2/(a^2-b^2-c^2) + b^2/(b^2-c^2-a^2) + c^2/(c^2-b^2-a^2)
Bài 2: Cho abc=2; rút gọn A= a/(ab+a+2) + b/(bc+b+1) + 2c/(ac+2c+2)
Rút gọn biểu thức A= 2/a-b+2/b-c+2/c-a+(a-b)^2+(b-c)^2+(c-a)^2/ (a-b)(b-c)c-a)
Rút gọn:
a) (a+b+c)^2-(a+b)^2-(a+c)^2-(b+c)^2
b) (a+b+c)^2+(a-b+c)^2+(a+b-c)^2+(-a+b+c)^2
Rút Gọn phân thức sau: {a^3(b^2-c^2)+b^3(c^2-a^2)+c^3(a^2-b^2)}/{a^2(b-c)+b^2(c-a)+c^2(a-b)}
Cho \(x=\dfrac{1}{a};y=\dfrac{1}{b};z=\dfrac{1}{c}\)
Rút gọn \(A=\dfrac{a^2b^2}{\left(a^3+b^3\right)c^2}\)
rút gọn biểu thức (a+b+c)^2 +(b+c-a)^2+(c+a-b)^2+(a+b-c)^2
