Here are the steps required for Multiplying Two Binomials Using the FOIL method:

Step 1: The FOIL method is a technique used to help remember the steps required to multiply two binomials. Remember that when you multiply two terms together you must multiply the coefficient (numbers) and add the exponents. The FOIL method is shown in the diagram below.

FOIL Diagram
Step 2: Combine like terms (if you can).

Example 1 – Multiply: (5x – 3)(2x + 7)

Step 1: Multiply each term in the first binomial with each term in the second binomial using the FOIL method as shown.
Step 1
Step 2: Combine like terms.
Step 2

Example 2 – Multiply: (4x – 5)(3x – 8)

Step 1: Multiply each term in the first binomial with each term in the second binomial using the FOIL method as shown.
Step 1
Step 2: Combine like terms.
Step 2

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Example 3 – Multiply: (6x + 5y)(2x + 3y)

Step 1: Multiply each term in the first binomial with each term in the second binomial using the FOIL method as shown.
Step 1
Step 2: Combine like terms.
Step 2

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Example 4 – Multiply: (3x2 + 4)(7x – 2)

Step 1: Multiply each term in the first binomial with each term in the second binomial using the FOIL method as shown.
Step 1
Step 2: Combine like terms. In this case, there are no like terms.
Step 2

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Example 5 – Multiply: (2x3 – 3)(4x3 – 1)

Step 1: Multiply each term in the first binomial with each term in the second binomial using the FOIL method as shown.
Step 1
Step 2: Combine like terms.
Step 2

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