If (9x - 4)(9x + 4) = ax² - b, what is the value of a?

Solution:

Given, (9x - 4)(9x + 4) = ax² - b

From algebraic identities:

We know, (a + b)(a - b) = a² - b²

Now, 81x² + 36x - 36x - 16 = ax² - b

81x² - 16 = ax² - b

So, ax² = 81x²

a = 81

-b = -16

b = 16

Therefore, the value of a is 81.

Example:

If (16x - 9)(16x + 9) = ax² - b, what is the value of a?

Solution:

Given, (16x - 9)(16x + 9) = ax² - b

We know, (a + b)(a - b) = a² - b²

Now, 256x² + 144x - 144x - 81 = ax² - b

256x² - 81 = ax² - b

So, ax² = 256x²

a = 16

-b = -81

b = 81

Therefore, the value of a is 16.

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If (9x - 4)(9x + 4) = ax² - b, what is the value of a?

Summary:

If (9x - 4)(9x + 4) = ax² - b, the value of a is 81.