19Rozłóż na czynniki

Wzory skróconego mnożenia, z jakich będę korzystać: a^2-2ab+b^2=(a-b)^2 a^2+2ab+b^2=(a+b)^2 a^2-b^2=(a-b)(a+b) a^3+b^3=(a+b)(a^2-ab+b^2) a) y^2+2xy-3x^2=y^2+2xy+x^2-4x^2=(y+x)^2-(2x)^2=(y+x-2x)(y+x+2x)=(y-x)(y+3x) b) x^2-xy-2y^2=x^2-4xy+y^2+3xy-6y^2=(x-2y)^2+3y \cdot (x-2y)=(x-2y)(x-2y+3y)=(x-2y)(x+y) c) x^2+8xy+15y^2=x^2+8xy+16y^2-y^2=(x+4y)^2-y^2=(x+4y+y)(x+4y-y)=(x+5y)(x+3y) d) x^2-13x+12=x^2-13x+\frac{169}{4}-\frac{121}{4}=(x-\frac{13}{2})^2-(\frac{11}{2})^2=(x-\frac{13}{2}-\frac{11}{2})(x-\frac{13}{2}+\frac{11}{2})=(x-12)(x-1) e) x^5-4x^3+x^2-4=x^3 \cdot (x^2-4)+x^2-4=(x^3+1)(x^2-4)=(x+1)(x^2-x+1)(x-2)(x+2)