Question

can any one please solve it step by step ❓❓​

Answer 1

Using the general binomial theorem , we have:

(a+b)³ = ³C₀ a³b⁰ + ³C₁ a²b+ ³C₂ ab² + ³C₃

∴ (a+b)³ = a³+3a²b+3ab²+b³

Using the general trinomial theorem, we have:

$(a + b + c) ^{2} = \sum _{i + j + k = 2} [\binom{2}{i,j,k} {a}^{i} {b}^{j} {c}^{k} ]$

∴ (a+b+c)² = a²+b²+c²+2(ab+bc+ac)

So,

Using the first expansion:

$( \frac{4x}{3y } + \frac{3y}{4x} ) ^{3} = ( \frac{4x}{3y} ) ^{3} + 3( \frac{4 x }{3y} . \frac{3y}{4x} )( \frac{4x}{3y} + \frac{3y}{4x} ) + {( \frac{3y}{4x}) }^{3}$

$( \frac{4x}{3y} + \frac{3y}{4x} ) ^{3} = \frac{64 {x}^{3} }{27 {y}^{3} } + \frac{4x}{y} + \frac{9y}{4x} + \frac{27 {y}^{3} }{64 {x}^{3} }$

Using the second expansion :

$(a - b - 5) ^{2} = (a) ^{2} + ( - b) {}^{2} + ( - 5) {}^{2} + 2( - ab + 5b - 5a)$

$(a - b - 5) {}^{2} = {a}^{2} + {b}^{2} + 25 - 2ab - 10a + 10b$