Question

expand (2x+1/2x)^3
pls answer correctly and main ans not the steps thx​

Answer 1

$\large\bf\underline\red{Answer \: :-}$

Given : (2x + 1/2x)³

Here,

$\sf{ \frac{1}{2} x = \frac{x}{2} }$

Now,

Formula : (a + b)³ = a³ + 3ab(a + b) + b³

$\sf\longrightarrow{(2x) {}^{3} + 3 (2x) \bigg( \frac{x}{2} \bigg) \bigg(2x + \frac{x}{2} \bigg) + \bigg( \frac{x}{2} \bigg) {}^{3} } \\ \\ \sf\longrightarrow{8x {}^{3} + \frac{6x {}^{2} }{2} \times \frac{5x}{2} + \frac{x {}^3{} }{8} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bf\longrightarrow \red{8x {}^{3} + \frac{11x {}^{2} }{4} + \frac{x {}^{3} }{8} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

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Important identities

$\begin{gathered}\boxed{\begin{array}{c} \\ \tiny\bf{\dag}\:\underline{\frak{\rm{S}\frak{ome\:important\:algebric\:identities\:::}}} \\\\ \green{\bigstar}\:\rm \red{ (A+B)^{2} = A^{2} + 2AB + B^{2}} \\\\ \red{\bigstar}\rm\: \green{(A-B)^{2} = A^{2} - 2AB + B^{2}} \\\\ \orange{\bigstar}\rm\: \blue{A^{2} - B^{2} = (A+B)(A-B)}\\\\ \blue{\bigstar}\rm\: \orange{(A+B)^{2} = (A-B)^{2} + 4AB}\\\\ \pink{\bigstar}\rm\: \purple{(A-B)^{2} = (A+B)^{2} - 4AB}\\\\ \purple{\bigstar} \rm\: \pink{(A+B)^{3} = A^{3} + 3AB(A+B) + B^{3}}\\\\ \pink{\bigstar}\rm\:(A-B)^{3} = A^{3} - 3AB(A-B) - B^{3}\\\\ \bigstar\rm\: \red{A^{3} + B^{3} = (A+B)(A^{2} - AB + B^{2})} \\\\ \end{array}}\end{gathered}$