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Find the product. Simplify your answer. \newline(a+3)(a−3)(a + 3)(a - 3)

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Full solution

Q. Find the product. Simplify your answer. \newline(a+3)(a−3)(a + 3)(a - 3)
  1. Recognize pattern: Recognize the pattern in the expression (a+3)(a−3)(a + 3)(a - 3). This expression is in the form of (a+b)(a−b)(a + b)(a - b), which is a difference of squares. Difference of squares special case: (a+b)(a−b)=a2−b2(a + b)(a - b) = a^2 - b^2
  2. Identify values: Identify the values of aa and bb. In the expression (a+3)(a−3)(a + 3)(a - 3), aa is simply aa, and bb is 33.
  3. Apply formula: Apply the difference of squares formula to the expression (a+3)(a−3)(a + 3)(a - 3).\newlineUsing the formula (a+b)(a−b)=a2−b2(a + b)(a - b) = a^2 - b^2, we get:\newline(a+3)(a−3)=a2−32(a + 3)(a - 3) = a^2 - 3^2
  4. Calculate squares: Calculate the squares of aa and 33. a2a^2 remains as a2a^2 since we cannot simplify it further without knowing the value of aa. 323^2 is 99. So, (a+3)(a−3)=a2−9(a + 3)(a - 3) = a^2 - 9
  5. Write final form: Write the final simplified form of the product.\newlineThe product (a+3)(a−3)(a + 3)(a - 3) simplifies to a2−9a^2 - 9.

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