Question

सरळरूप द्या: (2a + b)³ - (2a - b)³

Answer 1

सरळरूप द्या: (2a + b)³ - (2a - b)³

सरळरूप
${x}^{3} - {y}^{3} = (x - y)( {x}^{2} + xy + {y}^{2} )$

$x = 2a+b \\ \\ y = 2a-b$
${(2a+b)}^{3} - {(2a-b)}^{3} \\ \\ = (2a+b - 2a+b)( {(2a+b)}^{2} +(2a+b)(2a-b) + {(2a-b)}^{2} ) \\ \\ = 2b(4 {a}^{2} + {b}^{2} +4ab + 4{a}^{2} - {b}^{2} + 4 {a}^{2} + {b}^{2} -4ab) \\ \\ =( 2b) (12 {a}^{2} + {b}^{2})$
सरळरूप:
${(2a+b)}^{3} - {(2a-b)}^{3} = ( 2b) (12 {a}^{2} + {b}^{2})$