Identify if the following equations are true or not:

$i) (2 a + 3 b) (a - b) = 2 a^{2} - 3 b^{2}$

$i i) (x + 5)^{2} = x^{2} + 25$

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Solution

If the equations hold true, LHS should be equal to RHS

$i) L H S = (2 a + 3 b) (a - b)$

$= 2 a^{2} - 2 a b + 3 a b - 3 b^{2}$

$= 2 a^{2} + a b - 3 b^{2} \neq 2 a^{2} - 3 b^{2} \neq R H S$

$i i) L H S = (x + 5)^{2}$

$= x^{2} + 25 + 2 (x) (5)$

$= x^{2} + 25 + 10 x \neq x^{2} + 25 \neq R H S$

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