Question

Please factorise it.

Answer 1

${a}^{4} - 7 {a}^{2} {b}^{2} - {18b}^{4} \\ \\ write \: - {7a}^{2} {b}^{2} \: as \: a \: difference \\ \\ {a}^{4} + 2 {a}^{2} {b}^{2} - 9 {a}^{2} {b}^{2} - {18b}^{4} \\ \\ factor \: out \: {a}^{2} \: from \: {a}^{4} + {2a}^{2} {b}^{2} \\ \\ and \: factor \: out \: - 9 {b}^{2} \: from \: - 9 {a}^{2} {b}^{2} - 18 {a}^{4}$

${a}^{2} ( {a}^{2} + 2 {b}^{2} ) - 9 {b}^{2} ( {a}^{2} + 2 {b}^{2} ) \\ \\ factor \: out \: {a}^{2} + 2 {b}^{2} \\ \\ ( {a}^{2} + {2b}^{2})( {a}^{2} - 9 {b}^{2} ) \\ \\ use \: {a}^{2} - {b}^{2} = (a - b)(a + b) \: and \: factorise \\ \\ ( {a}^{2} + {2b}^{2} )( {a}^{2} - {(3b)}^{2} ) \\ \\ ( {a}^{2} + 2 {b}^{2} )( {a}^{} - 3b)(a + 3b)$

Answer 2

Answer:

See the attachment:

Step-by-step explanation:

Hope it's help you.