Question

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

Answer 1

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