Question

Factorize = 9c^2-a^2+4ab-4b^2​

Answer 1

$\bf \underline {Solution :-}$

$9 {c}^{2} - {a}^{2} + 4ab - 4 {b}^{2}$

$= 9 {c}^{2} - ( {a}^{2} - 4ab + 4 {b}^{2} )$

$= {(3c)}^{2} - {(a - 2b)}^{2}$

$= (3c + a - 2b)(3c - a + 2b)$

$\bf \: Answer : (3c+a-2b)(3c-a+2b)$

$\bf \underline{Formulas \: \: which \: \: are \: \: used \: \: here :-}$

$• \: {(a - b)}^{2} = {a}^{2} - 2ab + {b}^{2}$

$• \: ( {a}^{2} - {b}^{2} ) = (a + b)(a - b)$

$\bf \underline{Important \: Formulas :-}$

$• \: 4ab = {(a + b)}^{2} - {(a - b)}^{2}$

$• \: {a}^{3} + {b}^{3} = (a + b)( {a}^{2} - ab + {b}^{2} )$

$• \: {a}^{3} - {b}^{3} = (a - b)( {a}^{2} + ab + {b}^{2} )$

$• \: (a + b)^{3} = {a}^{3} + 3 {a}^{2} b + 3a {b}^{2} + {b}^{3}$

$• \: (a - b)^{3} = {a}^{3} - 3 {a}^{2} b + 3a {b}^{2} - {b}^{3}$

$• \: {(a + b)}^{2} = {a}^{2} + 2ab + {b}^{2}$