Expanding the Expression: (5p  3q)(p + 7q)
This article will guide you through expanding the expression (5p  3q)(p + 7q) using the distributive property or FOIL method.
Understanding the Distributive Property
The distributive property states that multiplying a sum by a number is the same as multiplying each addend in the sum by the number and then adding the results.
In simpler terms, a(b + c) = ab + ac.
Expanding the Expression

Apply the distributive property:
 Multiply the first term of the first binomial, 5p, by each term in the second binomial:
 5p * p = 5p²
 5p * 7q = 35pq
 Multiply the second term of the first binomial, 3q, by each term in the second binomial:
 3q * p = 3pq
 3q * 7q = 21q²
 Multiply the first term of the first binomial, 5p, by each term in the second binomial:

Combine the terms:
 5p² + 35pq  3pq  21q²

Simplify by combining like terms:
 5p² + 32pq  21q²
Final Answer
Therefore, the expanded form of (5p  3q)(p + 7q) is 5p² + 32pq  21q².