Rút gọn biểu thức: \(A=\left(a^2+b^2+c^2\right)^2-\left(a^2-b^2+c^2\right)^2\)
Những câu hỏi liên quan
Rút gọn biểu thức: \(A=\dfrac{2}{a-b}+\dfrac{2}{b-c}+\dfrac{2}{c-a}+\dfrac{\left(a-b\right)^2+\left(b-c\right)^2+\left(c-a\right)^2}{\left(a-b\right).\left(b-c\right).\left(c-a\right)}\)
Rút gọn biểu thức sau
\(\frac{a^2\left(b-c\right)+b^2\left(c-a\right)+c^2\left(a-b\right)}{a^2\left(b-c\right)-b^2\left(c+a\right)-c^2\left(a-b\right)+2abc}\)
rút gọn biểu thức:
\(\left(a+b+c+d\right)^2+\left(a+c-c-d\right)^2+\left(a-b+c-d\right)^2+\left(a-b-c+d\right)^2\)
\(\left(a+b+c+d\right)^2+\left(a+b-c-d\right)^2+\left(a-b+c-d\right)^2+\left(a-b-c+d\right)^2\)(Sửa lại nha bn viết sai để)
Đặt x=a+b , y=c+d , z=a-b , t=c-d
Khi đó biểu thức bằng
\(\left(x+y\right)^2+\left(x-y\right)^2+\left(z+t\right)^2+\left(z-t\right)^2\)
\(=x^2+y^2+2xy+x^2+y^2-2xy+z^2+t^2+2zt+z^2+t^2-2zt\)
\(=2\left(x^2+y^2+z^2+t^2\right)=2\left[\left(a+b\right)^2+\left(a-b\right)^2+\left(c+d\right)^2+\left(c-d\right)^2\right]\)
\(=2(a^2+b^2-2ab+a^2+b^2-2ab+c^2+d^2+2cd+c^2+d^2-2cd)\)
\(=2\left(2a^2+2b^2+2c^2+2d^2\right)=4\left(a^2+b^2+c^2+d^2\right)\)
Đúng 0
Bình luận (0)
Rút gọn biểu thức \(A=\frac{a^2\left(b-c\right)+b^2\left(c-a\right)+c^2\left(a-b\right)}{a^4\left(b^2-c^2\right)+b^4\left(c^2-a^2\right)+c^4\left(a^2-b^2\right)}\)
13 tháng 11 2021 lúc 14:21
rút gọn biểu thức
a. \(\left(a+b+c\right)^2+\left(a+b-c\right)^2-2\left(a+b\right)^2\)
b. \(\left(a^2+b^2-c^2\right)^2-\left(a^2-b^2+c^2\right)^2\)
a.\(=a^2+b^2+c^2+2ab+2bc+2ac+a^2+b^2+c^2+2ab-2bc-2ac-2\left(a^2+2ab+b^2\right)=2a^2+2b^2+2c^2+4ab-2a^2-2ab-2b^2=2c^2+2ab\)
b. \(=\left(a^2+b^2-c^2-a^2+b^2-c^2\right)\left(a^2+b^2-c^2+a^2-b^2+c^2\right)=\left(2b^2-2c^2\right).2a^2=4a^2\left(b^2-c^2\right)=4a^2b^2-4a^2c^2\)
Đúng 1
Bình luận (1)
1/rút gọn biểu thức:
\(A=\frac{2}{a-b}+\frac{2}{b-c}+\frac{2}{c-a}+\frac{\left(a-b\right)^2+\left(b-c\right)^2+\left(c-a\right)^2}{\left(a-b\right)\left(b-c\right)\left(c-a\right)}\)
rút gọn biểu thức
\(\frac{a^2-bc}{\left(a+b\right)\left(a+c\right)}+\frac{b^2-ca}{\left(b+c\right)\left(b+a\right)}+\frac{c^2-ab}{\left(c+a\right)\left(c+b\right)}\)
Rút gọn biểu thức :
a . \(\left(a+b+c\right)^2+\left(a-b-c\right)^2+\left(b-c-a\right)^2+\left(c-a-b\right)^2\)
b . \(\left(a+b+c+d\right)^2+\left(a+b-c-d\right)^2+\left(a+c-b-d\right)^2+\left(a+d-b-c\right)^2\)
Rút gọn biểu thức
a. B = \(\left(\dfrac{a-b}{a^2+ab}-\dfrac{a}{b^2+ab}\right):\left(\dfrac{b^3}{a^3-ab^2}+\dfrac{1}{a+b}\right)\)
b. C = \(a:\left(b-2\right)-\left[\left(a^2+2a+1\right):\left(b^2-4\right)\right].\left[\left(b+2\right):\left(a+1\right)\right]\)
Rút gọn biểu thức
a. B = \(\left(\dfrac{a-b}{a^2+ab}-\dfrac{a}{b^2+ab}\right):\left(\dfrac{b^3}{a^3-ab^2}+\dfrac{1}{a+b}\right)\)
b. C = \(a:\left(b-2\right)-\left[\left(a^2+2a+1\right):\left(b^2-4\right)\right].\left[\left(b+2\right):\left(a+1\right)\right]\)