Question

Find the following products, answer qestion with photos​

Answer 1

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Answer 2

$\mathfrak{\large{\underline{\underline{Answer :-}}}}$

$\boxed{\bold{ \left[3 + \dfrac{5}{x} \right] \left[ 9 - \dfrac{15}{x} + \dfrac{25}{ {x}^{2} }\right] = 27 + \dfrac{125}{ {x}^{3} } }}$

$\mathfrak{\large{\underline{\underline{Explanation:-}}}}$

$(3 + \dfrac{5}{x})(9 - \dfrac{15}{x} + \dfrac{25}{ {x}^{2} })$

$9 \: can \: be \: written \: as \: {3}^{2}$

$\dfrac{15}{x} \: can \: be \: written \: as \: 3 \times \dfrac{5}{x}$

$\dfrac{25}{ {x}^{2} } \: can \: be \: written \: as \: {( \dfrac{5}{x}) }^{2}$

We know that,x³ + y³ = (x + y)(x² - xy - y²)

Here x = 3 , y = 5/x

$= {3}^{3} + {( \dfrac{5}{x}) }^{3}$

$= 27 + \dfrac{ {5}^{3} }{ {x}^{3} }$

$since \: {(\dfrac{a}{b})}^{m} = \dfrac{ {a}^{m} }{ {b}^{m} }$

$= 27 + \dfrac{125}{ {x}^{3} }$

$\boxed{\bold{ \left[3 + \dfrac{5}{x} \right] \left[ 9 - \dfrac{15}{x} + \dfrac{25}{ {x}^{2} }\right] = 27 + \dfrac{125}{ {x}^{3} } }}$

$\mathfrak{\large{\underline{\underline{Identity\:used :-}}}}$

x³ + y³ = (x + y)(x² - xy + y²)

$\mathfrak{\large{\underline{\underline{Extra\:Information:-}}}}$

What is an Identity ?

An equation is called an identity if it is satisfied by any value that replaces its variables

Some Important Identities

1) (x + y)² = x² + 2xy + y²

2) (x - y)² = x² - 2xy + y²

3) (x + y)(x - y) = x² - y²

4) (x + a)(x + b) = x² + (a + b)x + ab