Questions: Find each product. (8x-1)(2x-5)

Find each product. (8x-1)(2x-5)
Transcript text: Find each product. \[ (8 x-1)(2 x-5) \]
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Solution

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Solution Steps

To find the product of two binomials, we can use the distributive property, also known as the FOIL method (First, Outer, Inner, Last). This involves multiplying each term in the first binomial by each term in the second binomial and then combining like terms.

Step 1: Define the Binomials

We start with the binomials \( (8x - 1) \) and \( (2x - 5) \).

Step 2: Apply the Distributive Property

Using the distributive property (FOIL method), we calculate the product: \[ (8x - 1)(2x - 5) = 8x \cdot 2x + 8x \cdot (-5) + (-1) \cdot 2x + (-1) \cdot (-5) \]

Step 3: Perform the Multiplications

Calculating each term:

  • First: \( 8x \cdot 2x = 16x^2 \)
  • Outer: \( 8x \cdot (-5) = -40x \)
  • Inner: \( -1 \cdot 2x = -2x \)
  • Last: \( -1 \cdot (-5) = 5 \)
Step 4: Combine Like Terms

Now, we combine the like terms: \[ 16x^2 - 40x - 2x + 5 = 16x^2 - 42x + 5 \]

Final Answer

The product of the binomials is \[ \boxed{16x^2 - 42x + 5} \]

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