Ta có ;
a2(b - c) + b2(c - a) + c2(a - b) =a2(b- a) + a2(a - c) + b2(c -a) + c2(a - b)
=(a - b)(c2 - a2) - (c - a)(a2 - b2)
=(a - b)(c - a)(c + a) - (c - a)(a - b)(a + b)
=(a - b)(c - a)(c + a - a - b)
=(a - b)(c - a)(c - b)
Phan tich da thuc thanh nhan tu
A=\(\left(a+b+c\right)^2+\left(a+b-c\right)^2-4c^2\)
Phân tích đa thuc thah nhan tu
\(\left(a+b\right)\left(a^2-b^2\right)+\left(b+c\right)\left(b^2-c^2\right)+\left(c+a\right)\left(c^2-a^2\right)\)
phan tích da thuc thanh nhan tu
\(\text{a}b\left(\text{a}-b\right)+bc\left(b-c\right)+c\text{a}\left(c-\text{a}\right)\)
phan tich da thuc thanh nhan tu
ab(a-b)+bc(b-c) +ca(c-a)
\(x^4-3x^3y+3x^2y^2-z^3-xy^3\)
\(\left(a-b\right)^3+\left(b-c\right)^3+\left(c-a\right)^3\)
Giải pt
\(\frac{b-c}{\left(a-b\right)\left(a-c\right)}+\frac{c-a}{\left(b-c\right)\left(b-a\right)}+\frac{a-b}{\left(c-a\right)\left(c-b\right)}=\frac{2}{a-b}+\frac{2}{b-c}+\frac{2}{c-a}\)
phan tích nhan tử thanh nhan tử:
a)\(3x^2-12y^2\)
b)\(5xy^2-10xyt+5xt^2\)
c)\(x^3+3x^2+3x+1-27x^3\)
d)\(\text{a}^3x-\text{a}b+b-x\)
e)\(3x^2\left(\text{a}+b+c\right)+36xy\left(\text{a}+b+c\right)+108y^2\left(\text{a}+b+c\right)\)
f)\(\text{a}b\left(\text{a}-b\right)+bc\left(b-c\right)+c\text{a}\left(c-\text{a}\right)\)
g)\(\left(\text{a}+b+c\right)^3-\text{a}^3-b^3-c^3\)
h)\(4\text{a}^2b^2-\left(\text{a}^2+b^2-c^2\right)^2\)
Giải PT : \(\frac{\left(b-c\right)\left(1+a^2\right)}{x+a^2}+\frac{\left(c-a\right)\left(1+b^2\right)}{x+b^2}+\frac{\left(a-b\right)\left(1+c^2\right)}{x+c^2}=0\)
Rút gọn pt
\(D=\frac{\left(b-c\right)^3+\left(c-a\right)^3+\left(a-b\right)^3}{a^2.\left(b-c\right)+b^2.\left(c-a\right)+c^2.\left(a-b\right)}\)
Giai pt sau:
\(\frac{\left(b-c\right)\left(1+a\right)^2}{x+a^2}+\frac{\left(c-a\right)\left(1+b\right)^2}{x+b^2}+\frac{\left(a-b\right)\left(1+c\right)^2}{x+c^2}=0\)
