Question

please answer the question others will be reported ​

Answer 1

$\large\text{ \boxed{\bold{[Topic:\ Factorization]}} }$

Notice this polynomial contains only biquadratic and quadratic terms. This polynomial is translated into the difference of perfect squares.

$\large\text{ \boxed{\bold{[Step\ 1.]}} }$

Let's split the quadratic term.

$\large\cdots\longrightarrow x^{4}+y^{4}-18x^{2}y^{2}=(x^{4}-2x^{2}y^{2}+y^{4})-16x^{2}y^{2}$

$\large\cdots\longrightarrow x^{4}+y^{4}-18x^{2}y^{2}=(x^{2}-y^{2})^{2}-(4xy)^{2}$

$\large\text{ \boxed{\bold{[Step\ 2.]}} }$

Then, we are done with the question.

$\large\cdots\longrightarrow x^{4}+y^{4}-18x^{2}y^{2}=(x^{2}+4xy-y^{2})(x^{2}-4xy-y^{2})$

$\large\text{ \boxed{\bold{[Final\ answer]}} }$

$\large\text{ \cdots\longrightarrow\boxed{x^{4}+y^{4}-18x^{2}y^{2}=(x^{2}+4xy-y^{2})(x^{2}-4xy-y^{2})} }$