Question

factorize these allll.

Answer 1

$13) {a}^{2} xy + ab {x}^{2} + {b}^{2} xy + ab {y}^{2} \\ ax(ay + bx) + by(bx + ay) \\ ax(bx + ay ) + by(bx + ay) \\ (bx + ay)(ax + by) \: \: \: \: ans$
$14) \\ ( {2(2x - 3))}^{2} - ( 3{(y + 1))}^{2} \\( 2(2x - 3) + 3(y + 1))(2(2x - 3) - 3(y + 1)) \\ (4x - 6 + 3y + 3)(4x - 6 - 3y - 3) \\ (4x + 3y - 3)(4x - 3y - 9) \: \: \: ans$
$15) \\ ( {4 {x}^{2}) }^{2} - {(25)}^{2} \\ using \: identity \\ {a}^{2} - {b}^{2} = (a + b)(a - b) \\ (4 {x}^{2} + 25)(4 {x}^{2} - 25) \\ (4 {x}^{2} + 25)( {(2x)}^{2} - {5}^{2} ) \\ (4 {x}^{2} + 25)(2x + 5)(2x - 5) \: \: \: ans$
$16) {a}^{8} + {a}^{4} {b}^{4} + {b}^{8} + {a}^{4} {b}^{4} - {a}^{4} {b}^{4} \\ {a}^{8} + 2 {a}^{4} {b}^{4} + {b}^{8} - {a}^{4} {b}^{4} \\ ( { {a}^{4} + {b}^{4} )}^{2} - ( { {a}^{2} {b}^{2} )}^{2} \\ ( {a}^{4} + {b}^{4} - {a}^{2} {b}^{2} )( {a}^{4} + {b}^{4} + {a}^{2} {b}^{2} )$