Question

1. simplified form of x^4-81/x+3.

2. simplified form of (x^2yz)^2(xy^2z^2)/(xyz)^2.

Answer 1

1.
`(x^2+9)(x-3)`.

2.
`x^3y^2z^2`.

Explanation:

1. The given expression is

`(x^4-81)/(x+3)`

`((x^2)^2-(9)^2)/(x+3)`

`((x^2+9)(x^2-9))/(x+3)`
`[a^2-b^2=(a-b)(a+b)]`

`((x^2+9)(x^2-3^2))/(x+3)`

`((x^2+9)(x-3)(x+3))/(x+3)`
`[a^2-b^2=(a-b)(a+b)]`

`(x^4-81)/(x+3)=(x^2+9)(x-3)`

Therefore the simplified form of the given expression is
`(x^2+9)(x-3)`.

2. The given expression is

`((x^2yz)^2(xy^2z^2))/((xyz)^2)`

`((x^4y^2z^2)(xy^2z^2))/(x^2y^2z^2)`
`[(ab)^m=a^mb^m]`

`(x^5y^4z^4)/(x^2y^2z^2)`
`[x^mx^n=x^(m+n)]`

`x^3y^2z^2`
`[(x^m)/(x^n)=x^(m-n)]`

Therefore the simplified form of the given expression is
`x^3y^2z^2`.

Answer 2

#1. The problem ask to find the simplified form of the said equation, so in calculating it, you must first get is factored form and that is (x^2+9)(x^2-9)/x+3 then expand again, (x^2+9)(x+3)(x-3)/(x+3), then cancel the value and came up with an answer of (x^2+9)(x-3).
#2 In getting its answer you must follow the rule of a^m/a^n = a^m-n and then you will get the answer of y^2z^2x^3. I hope this would help