Question

(a+1)x⁴+a²x²y²+(a-1)y⁴​

Answer 1

Step-by-step explanation:

We have,

$(a + 1) {x}^{4} + {a}^{2} {x}^{2} {y}^{2} + (a - 1) {y}^{4}$

$= (a + 1) {x}^{4} + ( {a}^{2} - 1 + 1) {x}^{2} {y}^{2} + (a - 1) {y}^{4}$

$= (a + 1) {x}^{4} + (a + 1)(a - 1) {x}^{2} {y}^{2} + {x}^{2}{y}^{2} + (a - 1) {y}^{4}$

$= (a + 1) {x}^{2} ( {x}^{2} + (a - 1) {y}^{2}) + {y}^{2} ( {x}^{2} + (a - 1) {y}^{2} )$

$= ( {x}^{2} - {y}^{2} + a {y}^{2} )( {x}^{2} + {y}^{2} + a {x}^{2} )$