Question

Which expression is equivalent to the given polynomial expression?

(-4a2 – 36) + (-2ab – a2 + 2) + (-82 + 6ab)

OA. -3a2 + 4ab + 36

OB. -3a2 + 252 + 8ab + 36

O C. -5a2 + 4ab

36

OD -5a2 + 252 + 8ab + 36

Answer 1

The expression (-4a^2 - 36) + (-2ab - a^2 + 2) + (-82 + 6ab) is equivalent to -5a^2 + 4ab - 118.

Step-by-step explanation:

The expression (-4a^2 - 36) + (-2ab - a^2 + 2) + (-82 + 6ab) can be simplified by combining like terms.

Grouping the terms together, we have -4a^2 - a^2 - 2ab + 6ab - 36 + 2 - 82. Rearranging, we get -5a^2 + 4ab - 118.

Therefore, the expression is equivalent to -5a^2 + 4ab - 118.

Answer 2

The equivalent expression is:
`-5a^2 + 4ab + 116`

Step-by-step explanation:

An equivalent expression to the one given can be found removing first from the parenthesis, and then combining the like terms. So

`(-4a^2 - 36) + (-2ab - a^2 + 2) + (-82 + 6ab)`

Removing from the parenthesis

`-4a^2 - 36 - 2ab - a^2 + 2 - 82 + 6ab`

Combining the like terms:

`-4a^2 - a^2 - 2ab + 6ab - 36 + 2 - 82`

`-5a^2 + 4ab + 116`

The equivalent expression is:
`-5a^2 + 4ab + 116`