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\(VT=\frac{c-b}{\left(a-b\right)\left(c-a\right)}+\frac{a-c}{\left(a-b\right)\left(b-c\right)}+\frac{b-a}{\left(b-c\right)\left(c-a\right)}\)
\(=\frac{-\left(b-c\right)^2-\left(c-a\right)^2-\left(a-b\right)^2}{\left(a-b\right)\left(b-c\right)\left(c-a\right)}=\frac{-2a^2-2b^2-2c^2+2ab+2ac+2bc}{\left(a-b\right)\left(b-c\right)\left(c-a\right)}\)
\(=\frac{2ab-2ac+2bc-2b^2+2ab+2ac-2bc-2a^2-2ab+2ac+2bc-2c^2}{\left(a-b\right)\left(b-c\right)\left(c-a\right)}\)
\(=\frac{2\left(a-b\right)\left(b-c\right)+2\left(a-b\right)\left(c-a\right)+2\left(b-c\right)\left(c-a\right)}{\left(a-b\right)\left(b-c\right)\left(c-a\right)}\)
\(=\frac{2}{c-a}+\frac{2}{b-c}+\frac{2}{a-b}\)
\(\left(a+b-c\right)^2=\left(\left(a+b\right)-c\right)^2\)
\(=\left(a+b\right)^2+c^2-2\left(a+b\right)c\)
\(=a^2+b^2+2ab+c^2-2ac-2bc\)
\(=a^2+b^2+c^2+2ab-2bc-2ca\)
\(\left(a-b+c\right)^2=\left(\left(a-b\right)+c\right)^2\)
\(=\left(a-b\right)^2+c^2+2\left(a-b\right)c\)
\(=a^2+b^2-2ab+c^2+2ac-2bc\)
\(=a^2+b^2+c^2-2ab-2bc+2ca\)
\(\left(x-y+z\right)\left(x-y-z\right)=\left(\left(x-y\right)+z\right)\left(\left(x-y\right)-z\right)\)
\(=\left(x-y\right)^2-z^2\)
\(=x^2+y^2-2xy-z^2\)
( a + b - c )2 = [ ( a + b ) - c ]2
= ( a + b )2 - 2( a + b )c + c2
= a2 + b2 + c2 + 2ab - 2bc - 2ac
( a - b + c )2 = [ ( a- b ) + c ]2
= ( a - b )2 + 2( a - b )c + c2
= a2 + b2 + c2 - 2ab - 2bc + 2ca
( x - y + z )( x - y - z ) = [ ( x - y ) + z ][ ( x - y ) - z ]
= ( x - y )2 - z2
= x2 + y2 - z2 - 2xy
a)a7+7a^6b+21a^5b^2+35a^4b^3+21a^2b^5+7ab^6+b^7
b)a^10+10a^9b+45a^8b^2+120a^7b^3+210a^6b^4+252a^5b^5+210a^4b^6+120a^3b^7+45a^2b^8+10ab^9+b^10
c,d,e tuongtu
P/s:Ok you gioi, tui bt v nen dung dang cai thua mak ko hieu
a ) ( a + b ) 7 = a7 + 7a6b + 21a5b2 + 35a4b3 + 35a3b4 + 21a2b5 + 7ab6 + b7
b ) ( a + b ) 10 = a10 + 10a9b + 45a8b2 + 120a7b3 + 210a6b4 + 252a5b5 + 210a4b6 + 120a3b7 + 45a2b8 + 10ab9 + b10
c ) ( a + b ) 12 = a12 + 12a11b + 66a10b2 + 220a9b3 + 495a8b4 + 792a7b5 + 924a6b6 + 792a5b7 + 495a4b8 + 220a3b9 + 66a2b10 + 12ab11 + b12
d ) ( a + b ) 15 = a15 + 15a14b + 105a13b2 + 455a12b3 + 1365a11b4 + 3003a10b5 + 5005a9b6 + 6435a8b7 + 6435a7b8 + 5005a6b9 + 3003a5b10 + 1365a4b11 + 455a3b12 + 105a2b13 + 15ab14 + b15
HẰNG ĐẲNG THỨC CÒN LẠI BẠN TỰ LÀM NHÉ !!! MÌNH NGẠI ĐÁNH MÁY LẮM . 
a) \(\left(2x^3y-0,5x^2\right)^3\)
\(=\left(2x^3y\right)^3-3\left(2x^3y\right)^20,5x^2+3.2x^3y\left(0,5x^2\right)^2-\left(0,5x^2\right)^3\)
\(=8x^9y^3-6x^8y^2+1,5x^7y-0,125x^6\)
b) \(\left(x-3y\right)\left(x^2+3xy+9y^2\right)\)
\(=x^3-\left(3y\right)^3\)
\(=x^3-27y^3\)
c) \(\left(x^2-3\right)\left(x^4+3x^2+9\right)\)
\(=x^3-3^3\)
\(=x^3-27.\)
Mình gửi bạn trước câu a, b câu c mình cần xem lại đã nha
a, (a + b + c)^2 + (a - b - c)^2 +( b - c - a) ^2 + (c - a - b)^2
= (a + b + c)^2 + (a + b - c)^2 + (a - b - c)^2 + (a - b + c)^2
= (a + b)^2 + 2c(a + b) + c^2 + (a + b)^2 - 2c(a + b) + c^2 +
(a - b)^2 - 2c(a - b) + c^2 + (a - b)^2 + 2c(a - b) +c^2
= 2(a + b)^2 + 2c^2 + 2(a - b)^2 + 2c^2
= 2[(a + b)^2 + (a - b)^2] + 4c^2
=2(2a^2 + 2b^2) + 4c^2
= 4(a^2 + b^2 + c^2)
(a+b+c)2=(a+b)2+2(a+b)c+c2
=a2+2ab+b2+2ac+2bc+c2
(a+b-c)2=(a+b)2-2(a+b)c+c2
=a2+2ab+b2-2ab-2bc+c2
(a-b-c)2=(a-b)2-2(a-b)c+c2
=a2-2ab+b2-2ac+2bc+c2