Question

Please simply with proper explanation:(p – q) (p2 + pq + q2) = p3 – q3

Answer 1

Step-by-step explanation:

p(p2-q2)+q(p2-q2) + p(p2+q2) -q(p2+q2)

p3-pq2+qp2-q3+p3+pq2-qp2+q3

= 0

Answer 2

Answer:

(p – q) (p2 + pq + q2) = p3 – q3

Step-by-step explanation:

first multiply p with all:

p(p2 + pq + q2)

p3 + p2q + pq2

remember that when you multiply a p(1 variable) to any other variable then it adds one into its power if it is the same as p and simply adds as p if it is another variable like

p(y7)

=py7

p(p2)

=p3

p(x2y4p3)

=x2y4p4

now multiply with q

q(p2 + pq + q2)

qp2  +pq2 +q3

now subtract both.

(p3 + p2q + pq2)-(qp2  +pq2 +q3)

p3 + p2q + pq2 -qp2  -pq2 -q3

pq2-pq2 + p2q-qp2 + p3 - q3

= p3 - q3