Question

factorise
169b^4 - 100 b^2​

Answer 1

$\bf \underline{Solution:-}$

$169 {b}^{4} - 100 {b}^{2}$

$= ( {13b}^{2})^{2} - ( {10 b })^{2}$

$=( 13 {b}^{2} + 10b)(13 {b}^{2} - 10b)$

$\bf \underline{Formulas :-}$

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

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

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

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

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

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

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

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

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