Question

Show that (3x - 4)2 + 48x = (3x + 4)2.​

Answer 1

SOLUTION

TO PROVE

$\sf{ {(3x - 4)}^{2} + 48x = {(3x + 4)}^{2} }$

FORMULA TO BE IMPLEMENTED

We are aware of the formula that

$\sf{1. \: \: {(x + y)}^{2} = {x}^{2} + 2xy + {y}^{2} }$

$\sf{ 2. \: \: {(x - y)}^{2} = {x}^{2} - 2xy + {y}^{2} }$

PROOF

$\sf{ {(3x - 4)}^{2} + 48x }$

$\sf{ = {(3x )}^{2} - 2.3x.4 + {(4)}^{2} + 48x } \: \:( by \: formula \: 2)$

$\sf{ = 9{x}^{2} - 24x + 16 + 48x } \:$

$\sf{ = 9{x}^{2} + 24x + 16 } \:$

$\sf{ = {(3x )}^{2} + 2.3x.4 + {(4)}^{2} } \:$

$\sf{ = {(3x + 4 )}^{2} } \: \:( by \: formula \: 1)$

Hence proved

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