Question

using identities , show that (7xy+9z)^2 - (7xy- 9z)^2 =252 xy

please answer i will mark as brainliest

Answer 1

$\large\bf\underline{To\:prove:}$

$\bf{(7xy+9z)^2 -(7xy-9z)^2 = 252xyz}$

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$\large\bf\underline{Identities\:used:}$

ㅤㅤㅤ$\underline{\boxed{\large\bf\pink{(a+b)^2 =a^2 +b^2 +2ab}}}$

ㅤㅤㅤ$\underline{\boxed{\large\bf\pink{(a-b)^2=a^2 +b^2 -2ab}}}$

$\large\bf\underline{On\:solving\:for\:LHS}$

$\bf{⟼(7xy+9z)^2 -(7xy-9z)^2}$

$\bf{⟼49x^2 y^2 + 81z^2 + 126xyz-(49x^2 y^2 +81z^2 - 126xyz)}$

$\bf{⟼49x^2 y^2 + 81z^2 + 126xyz-49x^2 y^2 -81z^2 +126xyz}$

$\bf{⟼\cancel{49x^2 y^2}-\cancel{49x^2 y^2}+\cancel{81z^2}-\cancel{81z^2}+126xyz+126xyz }$

$\bf{⟼252xyz}$

ㅤㅤㅤㅤㅤ$\large\bf\underline{LHS=RHS}$

ㅤㅤ$\bigstar\boxed{\large\sf{\leadsto 252 xyz= 252xyz}}$

$\large\bf\underline{Hence\:Proved}$

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