[tex](a+b)^4=(a+b)^2\cdot (a+b)^2=(a^2+2ab+b^2)(a^2+2ab+b^2)=\\\\=a^2\cdot a^2+a^2\cdot 2ab+a^2\cdot b^2+2ab\cdot a^2+2ab\cdot 2ab+2ab\cdot b^2+b^2\cdot a^2+b^2\cdot 2ab+b^2\cdot b^2=\\\\=a^4 + 2a^3b+a^2 b^2+2a^3b +4a^2b^2 +2ab^3+ a^2b^2+ 2ab^3+b^4 = \\\\=a^4 +4a^3b+6a^2b^2 +4ab^3 +b^4[/tex]
