Question

HELP PLS EXPLAINNN THIS TO MEEE I DONT UNDERSTAND

Answer 1

The second option is the correct one.

Explanation:

The algebraic expression is as such:

`10x^(2)y+6x^(2)-7y^(2)-6`

Step 1: Looking at the first element

The first term/element of the final expression is
`10x^(2)y`.

Only like variables can be added or subtracted from each other (
`x` can be added to
`x` to give
`2x`, but
`x` added to
`y` doesn't yield a different result).

In the options, there are two terms which have the variables
`x^(2)y`:

`8x^(2)y` and
`2x^(2)y`.

In the first three options,
`8x^(2)y` is being added to
`2x^(2)y`, which would give a result of
`10x^(2)y`:

`8x^(2)y+2x^(2)y\\=(8+2)x^(2)y\\=10x^(2)y`

But the fourth option subtracts
`2x^(2)y` from
`8x^(2)y`, which wouldn't equal to
`10x^(2)y`, and so the fourth option isn't correct.

Step 2: Looking at the second element

The second term/element of the final expression is
`6x^(2)`.

In the options, there are two terms which have the variables
`x^(2)`:

`7x^(2)` and
`x^(2)`.

In the rest of the three options,
`x^(2)` is being subtracted from
`7x^(2)`, which would give a result of
`6x^(2)`:

`7x^(2)-x^(2)\\=(7-1)x^(2)\\=6x^(2)`

So, we can't eliminate any options based on this.

Step 3: Looking at the third element:

The same thing as the second element happens with
`-7y^(2)`, so we can't use it either.

Step 4: Looking at the 3x that are being cancelled out

We can see that the options contain the term
`3x`, even though it is nowhere to be seen in the final expression.

This means that
`3x` is subtracted from itself to produce a result of
`0` (
`3x-3x=0`), thus it is not present in the final expression.

In the second and third options, we can see that
`3x` is being subtracted from itself.

But, the first option has
`3x` being added to itself.
This would produce a result of
`6x`:

`3x+3x\\=(3+3)x\\=6x`

Which isn't present in the final expression.

Thus, the first option is also incorrect.

Step 5: Looking at the fourth element

The fourth term/element of the final expression is
`-6`.

In the options, there are two terms which are also integers:

`-2` and
`4`.

In the second option,
`4` is being subtracted from
`-2`, which would give a result of
`-6`:

`-2-4\\=-6`

But in the third option,
`4` is being subtracted from
`2`, which would give a result of
`-2` instead of
`-6`,
So, the third option is also wrong.