Question

simplify(5/2m+3/2n)2​

Answer 1

Answer:

5m+3n/mn

Step-by-step explanation:

(5/2m+3/2n)×2

taking common in denominator and cancelling 2

we get,

5/m + 3/n

LCM

5m+3n/mn

Answer 2

$\rm\bold{{Simplify \bigg( \dfrac{5}{2}m+\dfrac{3}{2}n}\bigg)^2}$

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$\rm\bold{ Identity\: used :}$

$\underline{\boxed{\rm(a + b)^2 = a^2 + 2ab + b^2 }}$

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$\longrightarrow\rm \bigg( \dfrac{5}{2}m + \dfrac{3}{2}n\bigg)$

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$\longrightarrow\rm\bigg(\dfrac{5}{2}m\bigg)^2 + 2\bigg(\dfrac{5}{2}m\times\dfrac{3}{2}n\bigg)+ \bigg(\dfrac{3}{2}n\bigg)^2$

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$\longrightarrow\rm\dfrac{25}{4}m^2 + \dfrac{15}{2}mn + \dfrac{9}{4}n^2$

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More:

Identity can be used to simplify as less calculations are required, they can also be used to factorise the expressions as opposite is also true.

Some more identities:

1. ( a - b )² = a² - 2ab + b²
2. ( a + b ) ( a - b) = a² - b²
3. ( a + b )( a² - ab + b² ) = a³ + b³
4. ( a - b )( a² + ab + b²) = a³ - b³