Question

(3x-1/2x+5/4)2 expand the following ​

Answer 1

$Expansion \: of \red{ \Big( 3x + \frac{1}{2x}+ \frac{5}{4}\Big)^{2}}$

/* By Algebraic Identity */

$\pink{ (a+b+c)^{2}}$

$\pink{ = a^{2}+b^{2}+c^{2}+2ab+2bc+2ca}$

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$= (3x)^{2}+\Big(-\frac{1}{2x}\Big)^{2}+\Big(\frac{5}{4}\Big)^{2}$

$+2\times (3x)\times \Big(-\frac{1}{2x}\Big) +2\times \Big(-\frac{1}{2x}\Big) \times \Big(\frac{5}{4}\Big) +2 \times \Big(\frac{5}{4}\Big)\times 3x$

$= 9x^{2}+\frac{1}{4x^{2} }+ \frac{25}{4} - 3 - \frac{5}{4x} + \frac{15x}{2}$

Therefore.,

$\red{Expansion \: of \:\Big( 3x + \frac{1}{2x}+ \frac{5}{4}\Big)^{2}}$

$\green{= 9x^{2}+\frac{1}{4x^{2} }+ \frac{25}{4}}$

$\green{- 3 - \frac{5}{4x} + \frac{15x}{2}}$

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