Question
Multiply using the rule for the product of the sum and difference of two terms. \[ (8 x+3)(8 x-3) \]
Ask by Gray Ruiz. in the United States
Mar 09,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The product is \( 64x^2 - 9 \).
Solution
1. Recognize the pattern for the product of the sum and difference of two terms:
\[
(a+b)(a-b)= a^2-b^2
\]
2. Here, let \( a = 8x \) and \( b = 3 \).
3. Apply the formula:
\[
(8x+3)(8x-3)= (8x)^2 - 3^2
\]
4. Compute each square:
\[
(8x)^2 = 64x^2 \quad \text{and} \quad 3^2 = 9
\]
5. Write the final answer:
\[
64x^2 - 9
\]
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Simplify this solution Beyond the Answer
To multiply \( (8x + 3)(8x - 3) \), we can use the special product formula for the difference of squares, which states that \( (a + b)(a - b) = a^2 - b^2 \). Here, \( a = 8x \) and \( b = 3 \). First, calculate \( a^2 \): \[ (8x)^2 = 64x^2 \] Next, calculate \( b^2 \): \[ 3^2 = 9 \] Now, apply the formula: \[ (8x + 3)(8x - 3) = (8x)^2 - 3^2 = 64x^2 - 9 \] So, the final result is: \[ 64x^2 - 9 \]
