From science to arts, IDNLearn.com has the answers to all your questions. Receive prompt and accurate responses to your questions from our community of knowledgeable professionals ready to assist you at any time.
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]