Answer:
1. [tex]3y^2+2y-11[/tex]
2. [tex]8y^{7}x^{5}z^2[/tex]
3. [tex]x^3-9x^2+14x+24[/tex]
Step-by-step explanation:
1. We have been given an expression [tex](-y^2-4y-8)-(-4y^2-6y+3)[/tex] and we are asked to subtract and simplify our given expression.
Using order of operations (PEMDAS), first of all let us remove parenthesis.
[tex]-y^2-4y-8+4y^2+6y-3[/tex]
Now let us group like terms.
[tex](-y^2+4y^2)+(-4y+6y)+(-8-3)[/tex]
Upon combining like terms our expression simplifies to:
[tex](3y^2)+(2y)+(-11)[/tex]
[tex]3y^2+2y-11[/tex]
Therefore, our expression simplifies to [tex]3y^2+2y-11[/tex].
2. We have been given an expression [tex](2x^2y^3z^2)*(4xy^4x^2)[/tex] and we are asked to multiply and simplify our given expression.
[tex](2x^2y^3z^2)*(4y^4x*x^2)[/tex]
[tex](2x^2y^3z^2)*(4y^4x^3)[/tex]
Using exponent property [tex]a^b*a^c=a^{b+c}[/tex] we will get,
[tex]2*4x^{2+3}y^{3+4}z^2[/tex]
[tex]8x^{5}y^{7}z^2[/tex]
[tex]8y^{7}x^{5}z^2[/tex]
Therefore, our given expression simplifies to [tex]8y^{7}x^{5}z^2[/tex].
3. We are asked to multiply and simplify our expression [tex](x-4)(x^2-5x-6)[/tex].
Using distributive property we will get,
[tex]x*x^2-5x*x-6*x-4*x^2-5x*-4-6*-4[/tex]
[tex]x^3-5x^2-6x-4x^2+20x+24[/tex]
Upon combining like terms we will get,
[tex]x^3+(-5x^2-4x^2)+(-6x+20x)+24[/tex]
[tex]x^3+(-9x^2)+(14x)+24[/tex]
[tex]x^3-9x^2+14x+24[/tex]
Therefore, our given expression simplifies to [tex]x^3-9x^2+14x+24[/tex].
