Question

use identities to factorise each of the following​

Answer 1

Step-by-step explanation:

x {}^{4} - 18x {}^{2} y {}^{2} + 81y {}^{4} \\ =x {}^{4} - (9 + 9)x {}^{2}y {}^{2} + 81y {}^{4} \\ = x {}^{4} - 9x {}^{2} y {}^{2} - 9x {}^{2}y {}^{2} + 81y {}^{4} \\ = x {}^{2}(x {}^{2} - 9y {}^{2}) - 9y {}^{2}(x {}^{2} - 9y {}^{2} ) \\ =(x {}^{2} - 9y {}^{2})(x {}^{2} - 9y {}^{2})