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

`(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`

Evaluate: (2

Evaluate: $(2 a + \frac{1}{2a}) (2 a - \frac{1}{2a})$

Sum

$(2 a + \frac{1}{2a}) (2 a - \frac{1}{2a})$

$= {(2 a)}^{2} - {(\frac{1}{2a})}^{2}$ ......[ ∵ (a − b) (a + b) = a²b²]

$= 4 a^{2} - \frac{1}{{4a}^{2}}$

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

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

Evaluate the following using identities:

(1.5x²− 0.3y²) (1.5x²+ 0.3y²)

if $x + \frac{1}{x} = 11$ , find the value of $x^{2} + \frac{1}{x^{2}}$

If a + b + c = 0 and a² + b² + c² = 16, find the value of ab + bc + ca.

Find the following product:

If 49a² − b = $(7 a + \frac{1}{2}) (7 a - \frac{1}{2})$ then the value of b is

Use identities to evaluate : (998)²

Evalute : ${(\frac{7}{8} x + \frac{4}{5} y)}^{2}$

If a - $\frac{1}{a}$ = 8 and a ≠ 0 find :
(i) $a + \frac{1}{a} (i i) a^{2} - \frac{1}{a^{2}}$

Use the direct method to evaluate :
(3x²+5y²) (3x²−5y²)

If $49 x^{2} - b = (7 x + \frac{1}{2}) (7 x - \frac{1}{2})$ , then the value of b is ______.