Question

Factorise a^4 + b^4 -a^2 b^2​

Answer 1

Answer:

$2*(b^{2}+8b-2)$

Answer 2

Step-by-step explanation:

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

this is because

a⁴+b⁴=a⁴+b⁴+2a²b²-2a²b²=(a²-b²)²+2a²b².

Now proceeding ahead, we get:

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