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

Answer:

$(p^{9} -25)$

$(g^{2} -36)$

Step-by-step 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