Question

4. Expand :
$(\frac{1}{4a} + 4a)^{2}$

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Answer 1

Answer:

Step-by-step explanation:

Given,

$\bigg(\dfrac{1}{4a} + 4a\bigg)^2$

To do :-

Expand it.

Solution :-

As the given expression is in the form of (x+ y)^2 we can apply the formula of (x+ y)^2 and we can expand that :-

Formula Used :-

$(x + y)^2 = x^2 + 2xy+ y^2$

Let's do :-

Here by comparing these both expressions we can substitute 1/4a in place of 'x' and 4a in place of 'y'.

$\bigg(\dfrac{1}{4a} + 4a\bigg)^2 =$

$\bigg(\dfrac{1}{4a}\bigg)^2 + 2\times\dfrac{1}{4a}\times4a + (4a)^2$

$= \bigg(\dfrac{1}{16a^2}\bigg) + 2 + 16a^2$

$= \dfrac{1}{16a^2} + 2 + 16a^2$

$= 16a^2 + \dfrac{1}{16a^2} + 2$

Know more :-

( x + y)^2 = x^2 + 2xy + y^2

(x - y)^2 = x^2 - 2xy + y^2