Question

Using identities,show that (7xy +9z)2 - (7xy - 9z)2 = 252xyz.

Answer 1

Appropriate Question

Using Identities, prove that

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

$\large\underline{\sf{Solution-}}$

Given algebraic expression is

$\rm :\longmapsto\: {(7xy + 9z)}^{2} - {(7xy - 9z)}^{2}$

We know,

$\rm :\longmapsto\:\boxed{\tt{ (a + b) ^{2} - (a - b)^{2} = 4 ab}}$

So, here,

$\red{\rm :\longmapsto\:a = 7xy}$

$\red{\rm :\longmapsto\:b = 9z}$

So, on substituting the values, we get

$\rm :\longmapsto\: {(7xy + 9z)}^{2} - {(7xy - 9z)}^{2}$

$\rm \:  =  \: 4 \times 7xy \times 9z$

$\rm \:  =  \: 4 \times 63xyz$

$\rm \:  =  \: 252xyz$

Hence,

$\rm\implies \: \boxed{\tt{ {(7xy + 9z)}^{2} - {(7xy - 9z)}^{2} = 252xyz}}$

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Additional Information

$\red{\rm :\longmapsto\:\boxed{\tt{ {(x - y)}^{2} = {x}^{2} - 2xy + {y}^{2}}}}$

$\red{\rm :\longmapsto\:\boxed{\tt{ {(x + y)}^{2} = {x}^{2} + 2xy + {y}^{2}}}}$

$\green{\rm :\longmapsto\:\boxed{\tt{ {(x + y)}^{3} = {x}^{3} + 3xy(x + y) + {y}^{3}}}}$

$\green{\rm :\longmapsto\:\boxed{\tt{ {(x - y)}^{3} = {x}^{3} - 3xy(x - y) - {y}^{3}}}}$

$\blue{\rm :\longmapsto\:\boxed{\tt{ {(x + y)}^{2} + {(x - y)}^{2} = 2( {x}^{2} + {y}^{2})}}}$

$\blue{\rm :\longmapsto\:\boxed{\tt{ {(x + y)}^{2} - {(x - y)}^{2} = 4xy}}}$

$\purple{\rm :\longmapsto\:\boxed{\tt{ {x}^{2} - {y}^{2} = x + y)(x - y) \: }}}$