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For each expression listed, is it a difference of squares? Explain yes or no and why or why not. Explain in enough detail so there is no doubt that it is or isn't a difference of squares. 1. y5 − 25 2. 9m2n2 − 121 3. p18 − q10 4. 16r2 − 27

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danielmaduroh

Explanation:

If we can write a polynomial in the form [tex]a^2-b^2[/tex], then we can factor it as:

[tex]a^2-b^2=(a-b)(a+b)[/tex]

In this problem, we have the following expressions:

[tex]1. \ y^5 - 25 \\ \\ 2. \ 9m^2n^2-121 \\ \\ 3. p^{18} - q^{10} \\ \\ 4. 16r^2 - 27[/tex]

  • For 1 and 4 we can't write this in the form [tex]a^2-b^2[/tex] so this is not a difference of squares.

  • For 2:

[tex]9m^2n^2-121 =3^2m^2n^2-11^2 \\ \\ =(3mn)^2-11^2 =(3mn-11)(3mn+11)[/tex]

So we could write 2 as a difference of squares.

  • For 3:

[tex]p^{18} - q^{10}=(p^9)^2-(q^5)^2=(p^9-q^5)(p^9+q^5) \\ \\ \\ Remember: \ (a^m)^n=a^{mn}[/tex]

So we could write 2 as a difference of squares.

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