Question

Question #bad20

Answer 1

Answer 1:
`x(xy + 7)^3`

Answer 2:
`xz^5`

Answer 3:
`yx + x` or `x + x(y+4)` or `x + 2xy^3`

Answer 4:
`x + (y+2)z`

Explanation:

Answer 1:
`x(xy + 7)^3`

The question asks for a product of `x` and a factor that depends on `x`. Therefore you know that:

• You need to have multiplication of `x` and some other factor.
• Your other factor should change as you change `x`.

Hence, `x(xy + 7)^3` is your best bet, as you have multiplication, and your other factor - `(xy + 7)^3` - changes with `x`.

Answer 2:
`xz^5`

Again, you are asked for a product, but this time your factor does not depend on `x`. Therefore, you know:

• You must have multiplication of `x` and some other factor.
• Your other factor should not change as you change `x`.

So, `xz^5` is your best answer. You have multiplication, but `z` does not change with `x`.

Answer 3:
`yx + x` or `x + x(y+4)` or `x + 2xy^3`

Here, you're asked for a sum of two terms: `x`, and some multiple of `x`. So, you know that:

• You have addition of `x` and some other term.
• Your other term must be `x` multiplied by some factor (in terms of any other variable).

You have three answers that fulfill this criteria (listed above): all of them have `x` added to `x` times some factor (in terms of `y`).

Answer 4:
`x + (y+2)z`

Here, you're again asked for a sum, but this time your other term must not depend on `x`. Therefore, you know:

• You have addition of `x` and some other term.
• Your other term must not have `x` in it.

`x + (y+2)z` is your best choice here. Note that you have only `y` and `z` as variables in your 2nd term, and neither of those depend on `x`, making this your best answer.

Hope that helps :)