Discover how IDNLearn.com can help you find the answers you need quickly and easily. Our Q&A platform offers reliable and thorough answers to help you make informed decisions quickly and easily.
Answer:
[tex](3+xz)(-3+xz)[/tex]
[tex](y^2-xy)(y^2+xy)[/tex]
Step-by-step explanation:
The Difference of Squares
Any difference of two squared monomial results in a factored form like shown below:
[tex]a^2-b^2=(a-b)(a+b)[/tex]
Similarly:
[tex](a-b)(a+b)=a^2-b^2[/tex]
For a product of binomials to be a difference of squares, they must be in the described form.
------------------------
(x-y)(y-x) can be rewritten as:
-(x-y)(x-y)
Since both binomials are identicals, the product will not result in a difference of squares.
-----------------------
(6-y)(6-Y)
Since both binomials are identicals, the product will not result in a difference of squares.
-----------------------
(3+xz)(-3+xz) can be rewritten as:
(xz+3)(xz-3). This product is a sum multiplied by a difference of the very same terms, thus the result is a difference of squares:
[tex](3+xz)(-3+xz)=(xz)^2-9[/tex]
-----------------------
[tex](y^2-xy)(y^2+xy)[/tex]. This product is a sum multiplied by a difference of the very same terms, thus the result is a difference of squares:
[tex](y^2-xy)(y^2+xy)=y^4-(xy)^2[/tex]
-----------------------
Summarizing:
(3+xz)(-3+xz)
[tex](y^2-xy)(y^2+xy)[/tex]