fill in the blank: p^3+q^3=(p+q) ( )?

(p^2 - pq + q^2)

Use the "sum of cubes" formula. You might also want to take the time to learn the "difference of cubes" and "difference of squares" formulas too. This will save you a lot of time in the future.

The answer by the way is:

p^2 - pq + q^2

= (p+q)(p^2 +pq +q^2)

a^3 + b^3 ≡ (a + b)(a^2 - ab + b^2)

p^3 + q^3
= (p + q)(p^2 - pq + q^2)

p^2-pq+q^2

REMEMBER: a^3 + b^3 = (a + b)(a^2 - ab + b^2)

p^3+q^3 = (p+q)(p²-pq+q²)
and
p^3-q^3 = (p-q)(p²+pq+q²)

The acronym for a sum or difference of cubes is SOAP
you'll notice the pattern is (p ? q)(p² ? pq ? q²)
So how do your figure out the ?, use SOAP
S - Same sign as what was between the original cubes
O - Opposite sign that was between the original cubes
AP - Last sign is Always Positive.

(p^2-pq+q^2)
========================================
(p+q)(p^2-pq+q^2)=p^3-p^2q+pq^2+p^2q-pq^2+q^3=
=p^3+q^3
I had to double check it,I studied the identities almost
45 years ago.I am almost 60 years old now.
GOOD LUCK.

p^3+q^3=(p+q)(p^2-pq+q^2) answer//