Questions: Find the product using the FOIL method. (4x+9)(8x-5) (4x+9)(8x-5)=

Find the product using the FOIL method. (4x+9)(8x-5) (4x+9)(8x-5)=
Transcript text: Find the product using the FOIL method. \[ \begin{array}{c} (4 x+9)(8 x-5) \\ (4 x+9)(8 x-5)= \end{array} \]
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Solution

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Solution Steps

To find the product of two binomials using the FOIL method, we multiply the First terms, the Outer terms, the Inner terms, and the Last terms, and then sum all these products. Specifically, for the expression \((4x + 9)(8x - 5)\), we will calculate:

  1. First: Multiply the first terms of each binomial: \(4x \times 8x\).
  2. Outer: Multiply the outer terms: \(4x \times -5\).
  3. Inner: Multiply the inner terms: \(9 \times 8x\).
  4. Last: Multiply the last terms: \(9 \times -5\).

Finally, we sum all these products to get the expanded form of the expression.

To solve the given problem using the FOIL method, we will follow the steps outlined below:

Step 1: Apply the FOIL Method

The FOIL method stands for First, Outer, Inner, and Last, which refers to the terms in each binomial that we need to multiply together.

Given the expression: \[ (4x + 9)(8x - 5) \]

  • First: Multiply the first terms in each binomial: \[ 4x \cdot 8x = 32x^2 \]

  • Outer: Multiply the outer terms in the product: \[ 4x \cdot (-5) = -20x \]

  • Inner: Multiply the inner terms: \[ 9 \cdot 8x = 72x \]

  • Last: Multiply the last terms in each binomial: \[ 9 \cdot (-5) = -45 \]

Step 2: Combine Like Terms

Now, we combine all the terms obtained from the FOIL method: \[ 32x^2 - 20x + 72x - 45 \]

Combine the like terms \(-20x\) and \(72x\): \[ 32x^2 + 52x - 45 \]

Final Answer

The product of the binomials using the FOIL method is: \[ \boxed{32x^2 + 52x - 45} \]

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