a
4
+
b
4
−
2
a
2
b
2
−
c
4
+
a
2
−
b
2
+
c
2
=
=
a
2
a
2
+
b
2
b
2
−
a
2
b
2
−
a
2
b
2
−
c
2
c
2
+
a
2
−
b
2
+
c
2
+
a
2
c
2
−
a
2
c
2
+
c
2
b
2
−
c
2
b
2
=
=
a
2
(
a
2
−
b
2
+
c
2
)
−
b
2
(
a
2
−
b
2
+
c
2
)
+
(
a
2
−
b
2
+
c
2
)
−
c
2
(
a
2
−
b
2
+
c
2
)
=
=
(
a
2
−
b
2
−
c
2
+
1
)
(
a
2
−
b
2
+
c
2
)
alignc a^4 + b^4 - 2 a^2 b^2 - c^4 + a^2 - b^2 + c^2 "=" newline alignc "=" color red {a^2 a^2} color blue {+ b^2 b^2} color red {- a^2 b^2} color blue {- a^2 b^2} color maroon {- c^2 c^2} color green {+ a^2} color green {- b^2} color green {+ c^2} color red {+ a^2 c^2} color maroon { -a^2 c^2 + c^2 b^2} color blue {- c^2 b^2} "=" newline alignc "=" color red {a^2 ( a^2 - b^2 + c^2 )} color blue {-b^2 ( a^2 - b^2 + c^2 ) } color green {+( a^2 - b^2 + c^2 )} color maroon {-c^2 ( a^2 - b^2 + c^2 )} "=" newline
alignc "=" ( a^2 -b^2 -c^2 +1 ) ( a^2 - b^2 + c^2 )