Question

Determine whether the binomial can be written as a difference of two squares.

Answer with yes or no and explain your answer with words or by showing your work.

(a) p^9 - 25

(b) a^8 - 18

(c) g^2 - 36

Answer 1

`(p^(9) -25)`

`(g^(2) -36)`

Explanation:

Verify each case

case A) we have

`(p^(9) -25)`

we know that

`p^(9)=(p^(3))^(2)`

`25=(5)^(2)`

`(p^(9) -25)=(p^(3))^(2)-(5)^(2)` -----> is a difference of two squares

case B) we have

`(a^(8) -18)`

we know that

`a^(8)` -----> is not a perfect square

`18` -----> is not a perfect square

therefore

`(a^(8) -18)` -----> is not a difference of two squares

case C) we have

`(g^(2) -36)`

we know that

`g^(2)=(g)^(2)`

`36=(6)^(2)`

`(g^(2) -36)=(g)^(2)-(6)^(2)` -----> is a difference of two squares