If (8z-9) (8z+9) = az²-b, what is the value of a?

Solution:

Given (8z - 9) (8z + 9) = az²-b

This is of the form of the algebraic identity:

a²- b² = (a + b) (a - b)

Expand the terms in product

64z² -72z +72z -81 = az² -b

Here, -72z and +72z get cancelled

⇒ 64z² -81 = az² -b

By comparing the terms and the equal power of z and constant,

We get, a = 64 and b = 81

If (8z-9) (8z+9) = az²-b, what is the value of a?

Summary:

If (8z-9) (8z+9) = az²-b, the value of a is 64.