Question

Разложите на множители х^2 - a^2 x + 1/4 (a^4 - b^4)

Answer 1

$x^2-a^2x+frac{1}{4}(a^4-b^4)=\\ x^2-a^2x+frac{a^4}{4}-frac{b^4}{4}=\\ (x^2-a^2x+frac{a^4}{4})-frac{b^4}{4}=\\ (x^2-2*x*frac{a^2}{2}+(frac{a^2}{2})^2)-(frac{b^2}{2})^2=\\ (x-frac{a^2}{2})^2-(frac{b^2}{2})^2=\\ (x-frac{a^2}{2}+frac{b^2}{2})(x-frac{a^2}{2}+frac{b^2}{2})$