simplify: 4pq(3-q) + 2p(q-3) - 7q(p - 2pq) - 2p(5q^2 + 3)
the final result contains how many terms?
4pq(3-q) + 2p(q-3) - 7q(p - 2pq) - 2p(5q^2 + 3) =
12pq -4pq2 + 2pq - 6p - 7pq + 14pq2 - 10pq2 - 6p group like terms
[12 pq + 2pq - 7pq ] + [ -4pq2 + 14pq2 - 10pq2] + [ -6p - 6p] = terms in the middle set of brackets "cancel"........simplify the terms in the other two sets of brackets.......and we're left with.....
7pq - 12p → two terms
Simplify the following:
4 p q (3-q)+2 p (q-3)-7 q (p-2 p q)-2 p (5 q^2+3)
Factor p out of p-2 p q:
4 p q (3-q)+2 p (q-3)-7 q p (1-2 q)-2 p (5 q^2+3)
4 p q (3-q) = 12 p q-4 p q^2:
12 p q-4 p q^2+2 p (q-3)-7 q p (1-2 q)-2 p (5 q^2+3)
2 p (q-3) = 2 p q-6 p:
12 p q-4 p q^2+2 p q-6 p-7 q p (1-2 q)-2 p (5 q^2+3)
-7 p q (1-2 q) = 14 p q^2-7 p q:
12 p q-4 p q^2-6 p+2 p q+14 p q^2-7 p q-2 p (5 q^2+3)
-2 p (5 q^2+3) = -6 p-10 p q^2:
12 p q-4 p q^2-6 p+2 p q-7 p q+14 p q^2+-6 p-10 p q^2
Grouping like terms, 12 p q-4 p q^2-6 p+2 p q-7 p q+14 p q^2-6 p-10 p q^2 = (12 p q+2 p q-7 p q)+(-6 p-6 p)+(-4 p q^2+14 p q^2-10 p q^2):
(12 p q+2 p q-7 p q)+(-6 p-6 p)+(-4 p q^2+14 p q^2-10 p q^2)
12 (p q)+2 (p q)-7 (p q) = 7 (p q):
7 p q+(-6 p-6 p)+(-4 p q^2+14 p q^2-10 p q^2)
-6 p-6 p = -12 p:
7 p q+-12 p+(-4 p q^2+14 p q^2-10 p q^2)
-4 (p q^2)+14 (p q^2)-10 (p q^2) = 0:
7 p q-12 p
Factor p out of 7 p q-12 p:
Answer: | p (7q-12)
4pq(3-q) + 2p(q-3) - 7q(p - 2pq) - 2p(5q^2 + 3) =
12pq -4pq2 + 2pq - 6p - 7pq + 14pq2 - 10pq2 - 6p group like terms
[12 pq + 2pq - 7pq ] + [ -4pq2 + 14pq2 - 10pq2] + [ -6p - 6p] = terms in the middle set of brackets "cancel"........simplify the terms in the other two sets of brackets.......and we're left with.....
7pq - 12p → two terms