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(5p-3q)(p+7q)

2 min read Jun 16, 2024
(5p-3q)(p+7q)

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

  1. 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

  2. Combine the terms:

    • 5p² + 35pq - 3pq - 21q²

  3. Simplify by combining like terms:

    • 5p² + 32pq - 21q²

Final Answer

Therefore, the expanded form of (5p - 3q)(p + 7q) is 5p² + 32pq - 21q².

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