Question

Please help! 3 Questions please show how you solved the problem

1. Subtract & simplify (–y2 – 4y – 8) – (–4y2 – 6y + 3)

2.Multiply and simplify 2x2y3z2 · 4xy4x2

3.Multiply and simplify (x – 4) (x2 – 5x – 6)

Answer 1

1.
`3y^2+2y-11`

2.
`8y^(7)x^(5)z^2`

3.
`x^3-9x^2+14x+24`

Explanation:

1. We have been given an expression
`(-y^2-4y-8)-(-4y^2-6y+3)` and we are asked to subtract and simplify our given expression.

Using order of operations (PEMDAS), first of all let us remove parenthesis.

`-y^2-4y-8+4y^2+6y-3`

Now let us group like terms.

`(-y^2+4y^2)+(-4y+6y)+(-8-3)`

Upon combining like terms our expression simplifies to:

`(3y^2)+(2y)+(-11)`

`3y^2+2y-11`

Therefore, our expression simplifies to
`3y^2+2y-11`.

2. We have been given an expression
`(2x^2y^3z^2)*(4xy^4x^2)` and we are asked to multiply and simplify our given expression.

`(2x^2y^3z^2)*(4y^4x*x^2)`

`(2x^2y^3z^2)*(4y^4x^3)`

Using exponent property
`a^b*a^c=a^(b+c)` we will get,

`2*4x^(2+3)y^(3+4)z^2`

`8x^(5)y^(7)z^2`

`8y^(7)x^(5)z^2`

Therefore, our given expression simplifies to
`8y^(7)x^(5)z^2`.

3. We are asked to multiply and simplify our expression
`(x-4)(x^2-5x-6)`.

Using distributive property we will get,

`x*x^2-5x*x-6*x-4*x^2-5x*-4-6*-4`

`x^3-5x^2-6x-4x^2+20x+24`

Upon combining like terms we will get,

`x^3+(-5x^2-4x^2)+(-6x+20x)+24`

`x^3+(-9x^2)+(14x)+24`

`x^3-9x^2+14x+24`

Therefore, our given expression simplifies to
`x^3-9x^2+14x+24`.