\(\left(a+b+c\right)\left(ab+bc+ac\right)-abc\)
\(=\left(a+b+c\right)ab+\left(a+b+c\right)bc+\left(a+b+c\right)ac-abc\)
\(=a^2b+ab^2+abc+abc+b^2c+bc^2+a^2c+abc+ac^2-abc\)
\(=a^2b+ab^2+b^2c+bc^2+a^2c+ac^2+2abc\)
\(=ab\left(a+b\right)+\left(b^2c+abc\right)+\left(a^2c+abc\right)+\left(bc^2+ac^2\right)\)
\(=ab\left(a+b\right)+bc\left(a+b\right)+ac\left(a+b\right)+c^2\left(a+b\right)\)
\(=\left(a+b\right)\left(ab+bc+ac+c^2\right)\)
\(=\left(a+b\right)\left[b\left(a+c\right)+c\left(a+c\right)\right]\)
\(=\left(a+b\right)\left(b+c\right)\left(a+c\right)\)
=(a2b + abc + a2c) + (ab2 + b2c + abc) + ( abc+ bc2 + c2a) -abc
( bạn tự bỏ ngoặc rồi rút gọn nhé )
= (a2b + 2abc +c2b) + ( a2c + c2a) + ( ab2 + b2c)
= b(a+c)2 + ac(a+c) + b2(a+c)
= (a+c) [ b(a+c) + ac+b2 ]
= (a+c)(ab+b2 +bc +ac)
=(a+c)[b(a+b) +c(a+b)]
=(a+c)(a+b)(b+c)
