Question

докажите тождество
a4+4a3b+6a2b2+4ab3+b4=(a+b)4

Answer 1

$(a+b)^4=(a+b)^2(a+b)^2=(a^2+2ab+b^2)(a^2+2ab+b^2)=$
$a^4+2a^3b+a^2b^2+2a^3b+4a^2b^2+2ab^3+a^2b^2+2ab^3+b^4=\ a^4+4a^3b+6a^2b^2+4ab^3+b^4$