Answer:
[tex]\huge\boxed{1.\ 2y-11}[/tex]
[tex]\huge\boxed{2.\ 8x^5y^7z^2}[/tex]
[tex]\huge\boxed{3.\ x^3-9x^2+14x+24}[/tex]
Step-by-step explanation:
[tex]1.\\(-)(-)=(+)\\(-)(+)=(-)\\(+)(-)=(-)\\(+)(+)=(+)\\\\(-y^2-4y-8)-(-4y^2-6y+3)\\\\=-y^2-4y-8-(-4y^2)-(-6y)-3\\\\=-y^2-4y-8+4y^2+6y-3\\\\\text{combine like terms}\\\\=(-y^2+y^2)+(-4y+6y)+(-8-3)\\\\=2y-11[/tex]
[tex]2.\\\text{Use}\ a^n\cdot a^m=a^{n+m}\\\\2x^2y^3z^2\cdot4xy^4x^2=(2\cdot4)(x^2xx^2)(y^3y^4)z^2=8x^{2+1+2}y^{3+4}z^2\\\\=8x^5y^7z^2[/tex]
[tex]3.\\\text{Use FOIL:}\\\\(a+b)(c+d)=ac+ad+bc+bd\\\\(x-4)(x^2-5x-6)\\\\=(x)(x^2)+(x)(-5x)+(x)(-6)+(-4)(x^2)+(-4)(-5x)+(-4)(-6)\\\\=x^3-5x^2-6x-4x^2+20x+24\\\\\text{combine like terms}\\\\=x^3+(-5x^2-4x^2)+(-6x+20x)+24\\\\=x^3-9x^2+14x+24[/tex]
