Evaluate: (2"A"+1/"2a")(2"A"-1/"2a")

Evaluate: `(2"a"+1/"2a")(2"a"-1/"2a")`

Sum

`(2"a"+1/"2a")(2"a"-1/"2a")`

`=(2"a")^2-(1/"2a")^2` ......[ ∵ (a − b) (a + b) = a²b²]

`=4"a"^2-1/"4a"^2`

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Chapter 12: Identities - Exercise 12 (D) [Page 155]

Chapter 12 Identities
Exercise 12 (D) | Q 2.04 | Page 155

Simplify the following products:

`(1/2a - 3b)(1/2a + 3b)(1/4a^2 + 9b^2)`

Prove that a² + b² + c² − ab − bc − ca is always non-negative for all values of a, b and c

Write in the expand form: `(2x - y + z)^2`

Simplify of the following:

(x+3)³ + (x−3)³

The difference between two positive numbers is 5 and the sum of their squares is 73. Find the product of these numbers.

Use the direct method to evaluate :
(ab+x²) (ab−x²)

If a² - 3a - 1 = 0 and a ≠ 0, find : `"a" - (1)/"a"`

If `"r" - (1)/"r" = 4`; find : `"r"^4 + (1)/"r"^4`

Simplify:
(x + 2y + 3z)(x² + 4y² + 9z² - 2xy - 6yz - 3zx)

Expand the following:

(–x + 2y – 3z)²