Question

Разложить на множители:
a) 1/9*x^4+x^2y^2+9y^4
б) x^4-5x^2+4

Answer 1

а)$\frac{1}{9}x^4+x^2y^2+9y^4= (\frac{1}{3}x^2+3y^2)^2-x^2y^2=(\frac{1}{3}x^2+3y^2-xy)(\frac{1}{3}x^2+3y^2+xy)$

б)$x^4-5x^2+4=(x^4-4x^2+4)-x^2=(x^2-2)^2-x^2=(x^2-2-x)(x^2-2+x)=(x+1)(x-2)(x-1)(x+2)$