Question

[(5a+2)÷3]^2-[(2a-1)÷3]^2

Answer 1

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$[(5a + 2) \div 3] {}^{2} - [(2a - 1) \div 3] {}^{2}$

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$\underline{\pink{SOLUTION}}$ ➡

$[(5a + 2) \div 3] {}^{2} - [(2a - 1) \div 3] {}^{2} \\ \\ = ( \frac{5a + 2}{3} ) {}^{2} - ( \frac{2a - 1}{3} ) {}^{2} \\ \\ = \frac{(5a + 2) {}^{2} }{(3) {}^{2} } - \frac{(2a - 1) {}^{2} }{(3) {}^{2} } \\ \\ = [\frac{(5a) {}^{2} + 2 \times 5a \times 2 +( 2) {}^{2} }{9} ] -[\frac{(2a) {}^{2} - 2 \times 2a \times 1 + (1) {}^{2} }{9} ] \\ \\ = (\frac{25a {}^{2} +20a + 4 }{9} ) - ( \frac{4a {}^{2} - 4a + 1}{9} ) \\ \\ = \frac{25a {}^{2} + 20a + 4 - 4a {}^{2} + 4a - 1 }{9} \\ \\ = \frac{21a {}^{2} + 24a + 3}{9} \\ \\ = \frac{3(7a {}^{2} + 8a + 1) }{3 \times 3} \\ \\ = \frac{7a {}^{2} + 8a + 1}{3} \\ \\ = \frac{7a {}^{2} + 7a + a + 1}{3} \\ \\ = \frac{7a(a + 1) + 1(a + 1)}{3} \\ \\ = \frac{(a + 1)(7a + 1)}{3} \\ \\ = (\frac{a + 1}{3}) (\frac{7a + 1}{3} )$

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