Question

factorise--a4-11a2b2+b4​

Answer 1

SOLUTION

TO FACTORISE

$\sf{ {a}^{4} - 11 {a}^{2} {b}^{2} + {b}^{4} }$

EVALUATION

$\sf{ {a}^{4} - 11 {a}^{2} {b}^{2} + {b}^{4} }$

$\sf{ = {a}^{4} - 2 {a}^{2} {b}^{2} - 9 {a}^{2} {b}^{2} + {b}^{4} }$

$\sf{ = {a}^{4} - 2 {a}^{2} {b}^{2} + {b}^{4} - 9 {a}^{2} {b}^{2} }$

$\sf{ = { ({a}^{2}) }^{2} - 2 .{a}^{2} . {b}^{2} + {({b}^{2})}^{2} - 9 {a}^{2} {b}^{2} }$

$\sf{ = { ({a}^{2} - {b}^{2} ) }^{2} - 9 {a}^{2} {b}^{2} }$

$\sf{ = { ({a}^{2} - {b}^{2} ) }^{2} - {(3ab)}^{2} }$

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

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