Which shows how to factor 64 − 81a2

Question

?
A) 8
2 − (9a)2 = (8 − 3a)(8 + 3a)
B) 8
2 − (9a)2 = (8 − 9a)(8 + 9a)
C) 8
2 − (9a)2 = (8 − 3a)(8 − 3a)
D) 8
2 − (9a)2 = (8 − 9a)(8 − 9a)

Answer 1

To factor \(64 - 81a^2\), we recognize that this expression is a difference of squares.

The difference of squares formula is: \[ A^2 - B^2 = (A - B)(A + B) \]

In this case, we can identify:

• \(A = 8\) (since \(8^2 = 64\))
• \(B = 9a\) (since \((9a)^2 = 81a^2\))

Now, we apply the difference of squares formula: \[ 64 - 81a^2 = 8^2 - (9a)^2 = (8 - 9a)(8 + 9a) \]

Thus, the correct answer is: B) \(8^2 - (9a)^2 = (8 - 9a)(8 + 9a)\).