Which of the equations are true identities? A. (9k – 8)(9k + 8) = 81k2 + 64
B.(3m +2n)(6m – 4n) = 18m²
18m2 – 8n?
Choose 1

We have two expressions, let's see if they are true or not:

A: (9k - 8)*(9k + 8) = 81*k^2 + 64

To prove this, we only need to start in the left side and see if we can construct the right side:

(9k - 8)*(9k + 8) = (9k)*(9k) + (9*k)*8 - (9k)*8 + 8*(-8)

                         = (9k)^2 - 8^2

                         = 9^2*k^2 - 64  = 81*k^2 - 64

This is different than the thing in the original equation, then this one is not an identity.

B) (3m +2n)(6m – 4n) = 18m^2 – 8n

Same as before, we start at the left side and work it out.

(3m + 2n)*(6m - 4n) = (3m)*(6m) + (3m)*(-4n) + (2n)*(6m) + (2n)*(-4n)

                                = 18*m^2  -12*m*n + 12*m*n - 8*n^2

                                = 18*m^2 - 8*n^2

Notice that here we have an "n^2" while in the original equation we have only an "n".

This may be an error in the question and the exponent is missing, in that case, this equation would be an identity, but it is not as how is written in the question.

Then neither A nor B are correct.