Hey there!
When they are asking which of them are equal we need to solve a, b, c and d and see if they match up to 6x^2-2x-20.
Starting with A:
Expand:
3 x 2x^2 + 3 x -x + 3 x -6
Simplify 3 x 2x^2 to 6x^2
6x^2 + 3 x -x + 3 x -6
Regroup.
6x^2 = 3x + 3 x -6
Simplify 3 x -6 to -18
6x^2 - 3x - 18
That does not match up to 6x^2-2x-20.
A is INCORRECT.
Solving B:
Collect like terms:
4x - 2x + 2x^2 - 20
The ones bolded are like terms.
So, we now collect them and add them.
4x^2 + 2x^2 = 6x^2
6x^2 - 2x - 20
That matches up with 6x^2-2x-20.
B is CORRECT.
Solving C:
Multiply the parentheses then multiply:
6x^2-12x+10x-20
Collect like terms:
6x^2 - 2x - 20
This matches up with 6x^2-2x-20.
Thus, C is CORRECT.
Solving D:
Multiply the terms in the parentheses by -2:
6x^2 - 2x - 2 x 10
Multiply the numbers:
6x^2 - 2x - 20
This also matches up with 6x^2 - 2x - 20 / they are equal.
Thus, D is also CORRECT.
Therefore, our answers are:
B, C, D
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