Question

use suitable identities and solve the following:
a)
$a) \: (7a - 9b)(7a - 9b) \\ \\b) \: (6x - 7)(6x + 7) \\ \\ c) (2 {a}^{2} + 9)(2 {a}^{2} + 5) \\ \\ d)(x + 3)(x + 7)$
​

Answer 1

$\tt \: \: (7a - 9b)(7a - 9b) \\ \sf = {(7a)}^{2} + {(9b)}^{2} - 2(7a)(9b) \\ \bf= \red{ {49a}^{2} + {81b}^{2} - 126ab}$

$\tt \: \: (6x - 7)(6x + 7) \\ \sf = {(6x)}^{2} - {(7)}^{2} \\ \bf = \red{ {36x}^{2} - 49}$

$\tt \: \: (2 {a}^{2} + 9)(2 {a}^{2} + 5) \\ \rm = {( {2a }^{2} )}^{2} + (9 + 5) {2a}^{2} + 9(5) \\ = \bf \red{ {2a}^{4} + {28a}^{2} + 45}$

$\tt \: \: (x + 3)(x + 7) \\ = \rm {(x)}^{2} + (7 + 3)x + 3(7) \\ = \bf \red{ {x}^{2} + 10x + 21}$