Question

do this using this identities

Answer 1

Answer:

(i) $4x^{2}y^{2}$

(ii) $50x^{2}+242$

Step-by-step explanation:

$(i)\\ (x^{2} +y^{2})^{2} - (x^{2}-y^{2})^{2}\\=((x^{2})^{2}+2(x^{2})(y^{2})+(y^{2})^{2}) - ((x^{2})^{2} - 2 (x^{2})(y^{2})+(y^{2})^{2}\\= (x^{4} + 2x^{2}y^{2} + y^{4}) - (x^{4} -2x^{2}y^{2}+y^{4})\\= (x^{4}+2x^{2}y^{2}+y^{4}-x^{4}+2x^{2}y^{2}-y^{4})\\= 4x^{2}y^{2}$

$(ii)$

$= (5x+11)^{2} + (5x-11)^2\\= ((5x)^{2}+2(5x)(11)+(11)^{2}) + ((5x)^{2} -2(5x)(11)+(11)^{2})\\= (25x^{2}+110x +121) + (25x^{2}-110x+121)\\= 25x^{2}+110x+121+25x^{2}-110x+121\\= 50x^{2}+242$