Question

Verify that (3x + 5y)2 – 30xy = (3x)2 + (5y)2




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Answer 1

Answer:

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Step-by-step explanation:

$LHS \\ \\ (3x + 5y) {}^{2} - 30xy \\ \\ (3x) {}^{2} + (5y) {}^{2} + 2(3x)(5y) - 30xy \\ \\ (3x) {}^{2} + (5y) {}^{2} + 30xy - 30xy \\ \\ cancelling \: \: + 30xy \: \: and \: - 30xy, \\ we \: \: get\\ \\ (3x) {}^{2} + (5y) {}^{2} \\ \\ = RHS\\ \\ \\ Hence\: \: (3x + 5y) {}^{2} - 30xy=\\ (3x) {}^{2} + (5y) {}^{2}$

Answer 2

$\huge\rm\purple{answer:}$

${ }$

$\large\bf{{\underline{To~verify}}:}$

$\tt (3x + {5y)}^{2} - 30xy = {(3x)}^{2} + {(5y)}^{2}$

$\large\bf{{\underline{Here}}:}$

$\bf{LHS = } \tt{ {(3x + 5y)}^{2} - 30xy } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \tt \implies {(3x)}^{2} + 2(3x)(5y) + {(5y)}^{2} - 30xy \\ \tt \implies 9x^{2} + 2(15xy) + {25y}^{2} - 30xy \: \: \: \: \: \: \: \: \\ \tt \implies {9x}^{2} + \cancel{30xy} + {25y}^{2} \: \cancel{ - 30xy} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \tt \implies {9x}^{2} + {25y}^{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: ~~ \\ \tt \implies \purple{ \underline{ \underline{ \bf(3x)^{2} + (5y)^{2} = RHS}}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: ~~ \: \: \: \:$

$\large\bf{Hence~verified~~~{\huge{✓}}}$