Question

Show that (9x-3y)2+108xy = (9x+3y)2

Answer 1

Answer:

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Answer 2

SOLUTION

TO PROVE

$\sf{ {(9x - 3y)}^{2} + 108xy = {(9x + 3y)}^{2} }$

FORMULA TO BE IMPLEMENTED

1. (a + b)² = a² + 2ab + b²

2. (a - b)² = a² - 2ab + b²

EVALUATION

$\sf{ {(9x - 3y)}^{2} + 108xy}$

$\sf{ = {(9x)}^{2} - 2 \times 9x \times 3y + {(3y)}^{2} + 108xy}$

$\sf{ = 81{x}^{2} - 54xy+ 9{y}^{2} + 108xy}$

$\sf{ = 81{x}^{2} + 54xy+ 9{y}^{2} }$

$\sf{ = {(9x)}^{2} + 2 \times 9x \times 3y+ {(3y)}^{2} }$

$\sf{ = {(9x + 3y)}^{2} }$

Hence proved

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