Question

(3x + 7² – 84x = (3x - 7²​

Answer 1

${\large {\underline {\blue {\bf {Question}}}}}$

Prove that

$\sf \: {(3x + 7)}^{2} - 84x = {(3x - 7)}^{2}$

${\large {\underline {\blue {\bf {Answer}}}}}$

Consider

$\bf \longmapsto \: \bf \: LHS$

$\bf \longmapsto \: \bf \: {(3x + 7)}^{2} - 84x$

$\bf \longmapsto \: \bf \: {(3x)}^{2} + {(7)}^{2} + 2 \times 3x \times 7 - 84x$

$\bf \longmapsto \: \bf \: {9x}^{2} + 49 + 42x - 84x$

$\bf \longmapsto \: \bf \: {9x}^{2} + 49 - 42x$

Consider,

$\bf \longmapsto \: \bf \:RHS$

$\bf \longmapsto \: \bf \: {(3x - 7)}^{2}$

$\bf \longmapsto \: \bf \: {(3x)}^{2} + {7}^{2} - 2 \times 3x \times 7$

$\bf \longmapsto \: \bf \: {9x}^{2} + 49 - 42x$

Hence,

$\bf \longmapsto \: \bf \:LHS = RHS$

$\large{\boxed{\boxed{\bf{Hence, Proved}}}}$

Identities used :-

$\boxed{ \pink{\bf :\implies\:(x + y)^{2} \: = {x}^{2} + {y}^{2} + 2xy }}$

$\boxed{ \pink{\bf :\implies\:(x - y)^{2} \: = {x}^{2} + {y}^{2} - 2xy }}$