Expanding the Expression (5p + 3q)(2p + 5q)
This article will guide you through the process of expanding the expression (5p + 3q)(2p + 5q). We'll use the distributive property to achieve this.
Understanding the Distributive Property
The distributive property states that multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products. In simpler terms, it allows us to "distribute" the multiplication across the terms within parentheses.
Applying the Distributive Property

Multiply the first term of the first binomial by each term of the second binomial:
(5p + 3q)(2p + 5q) = 5p(2p + 5q) + 3q(2p + 5q)

Multiply the second term of the first binomial by each term of the second binomial:
5p(2p + 5q) + 3q(2p + 5q) = 5p(2p) + 5p(5q) + 3q(2p) + 3q(5q)

Simplify each term:
5p(2p) + 5p(5q) + 3q(2p) + 3q(5q) = 10p² + 25pq + 6pq + 15q²

Combine like terms:
10p² + 25pq + 6pq + 15q² = 10p² + 31pq + 15q²
Final Result
Therefore, the expanded form of (5p + 3q)(2p + 5q) is 10p² + 31pq + 15q².
This process can be applied to expanding any binomial multiplication expression. By understanding the distributive property and applying it stepbystep, you can simplify and solve complex algebraic expressions.