factors of a^2(b+c)+b^2(c+a)+c^2(a+b)+2abc
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a²(b + c ) + b² (c + a) + c² (a + b) + 2abc
= a²b + a²c + b²c + b²a + c²a + c²b + 2abc
= (a²b + 2abc + c²b) + a²c + b²a + b²c + c²a
= b(a² + 2ac + c²) + (a²c + ac²) + (b²a + b²c)
= b( a + c)² + ac(a + c) + b²(a + c)
= (a + c){b(a + c) + ac + b²}
= (a + c){ ba + bc + ac + b²)
= (a + c){(ba + ac ) + bc + b²}
= (a + c) { a( b + c) + b (c + b)}
= (a + c )(a + b)(b + c )
= (a + c )(c + b )( b + a )
= a²b + a²c + b²c + b²a + c²a + c²b + 2abc
= (a²b + 2abc + c²b) + a²c + b²a + b²c + c²a
= b(a² + 2ac + c²) + (a²c + ac²) + (b²a + b²c)
= b( a + c)² + ac(a + c) + b²(a + c)
= (a + c){b(a + c) + ac + b²}
= (a + c){ ba + bc + ac + b²)
= (a + c){(ba + ac ) + bc + b²}
= (a + c) { a( b + c) + b (c + b)}
= (a + c )(a + b)(b + c )
= (a + c )(c + b )( b + a )
...nice
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(a+c)(c+b)(b+a) gcycycy
Similar questions
= a^2 b+ a^2c + b^2 c+ ab^2+c^2a+bc^2+2abc
= a(b^2+ 2bc+c^2) + a^2 b+ a^2c + b^2 c +bc^2
= a(b+c)^2 + a^2(b+c) + bc(b+c)
= (b+c) [ a^2 +a(b+c)+ bc]
= (b+c) (a +b)(c+a)