Question

Plz Help 20 points Polynomials

1: Subtract and Simplify
(–y^2 – 4y – 8) – (–4y^2 – 6y + 3)
2: Multiply and Simplify
2x^2 y^3 z^2 · 4xy^4 x^2
3: Multiply and Simplify
(x – 4) (x2 – 5x – 6)

Answer 1

`\huge\boxed{1.\ 2y-11}`

`\huge\boxed{2.\ 8x^5y^7z^2}`

`\huge\boxed{3.\ x^3-9x^2+14x+24}`

Explanation:

`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`

`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`

`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`