Question

Which products result in difference of squares

(x-y)(y-x)

(6-y)(6-y)

(3+xz)(-3+xz)

(y^2-xy)(y^2+xy)

Answer 1

`(3+xz)(-3+xz)`

`(y^2-xy)(y^2+xy)`

Explanation:

The Difference of Squares

Any difference of two squared monomial results in a factored form like shown below:

`a^2-b^2=(a-b)(a+b)`

Similarly:

`(a-b)(a+b)=a^2-b^2`

For a product of binomials to be a difference of squares, they must be in the described form.

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(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.

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(6-y)(6-Y)

Since both binomials are identicals, the product will not result in a difference of squares.

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(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:

`(3+xz)(-3+xz)=(xz)^2-9`

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`(y^2-xy)(y^2+xy)`. This product is a sum multiplied by a difference of the very same terms, thus the result is a difference of squares:

`(y^2-xy)(y^2+xy)=y^4-(xy)^2`

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Summarizing:

(3+xz)(-3+xz)

`(y^2-xy)(y^2+xy)`