Szczegółowe wyjaśnienie:
[tex]u(x)=2x^6-ax^5+3x^2-x\\\\w(x)=2x^6-5x^5+2x^2+7\\\\u(x)+w(x)=(2x^6-ax^5+3x^2-x)+(2x^6-5x^5+2x^2+7)\\\\=2x^6-ax^5+3x^2-x+2x^6-5x^5+2x^2+7\\\\=(2x^6+2x^6)+(-ax^5-5x^5)+(3x^2+2x^2)-x+7\\\\=4x^6-(a+5)x^5+5x^2-x+7[/tex]
Stopień wielomianu u(x) + w(x) nie zależy od parametru a.
St.(u + w) = 6
[tex]a)\ (x-y)(x^2-y^2)(2x^3+y^3)=(x^3-xy^2-x^2y+y^3)(2x^3+y^3)\\\\=2x^6+x^3y^3-2x^4y^2-xy^5-2x^5y-x^2y^4+2x^3y^3+y^6\\\\=2x^6+y^6+3x^3y^3-2x^4y^2-2x^5y-x^2y^4-xy^5[/tex]
[tex]b)\ (x\sqrt3-y\sqrt2)(2x^2-xy\sqrt6+2x^2)=(x\sqrt3-y\sqrt2)(4x^2-xy\sqrt6)\\\\=4x^3\sqrt3-x^2y\sqrt{18}-4x^2y\sqrt2+xy^2\sqrt{12}\\\\=4x^3\sqrt3-x^2y\sqrt{9\cdot3}-4x^2y\sqrt2+xy^2\sqrt{4\cdot3}\\\\=4x^3\sqrt3-3x^2y\sqrt3-4x^2y\sqrt2+2xy^2\sqrt3[/tex]
