Simplify (3x+4)(3x-4)

Problem

(3⁢x+4)⁢(3⁢x−4) open paren 3 x plus 4 close paren times open paren 3 x minus 4 close paren

Solution

  1. Identify the pattern as a product of a sum and a difference, which follows the difference of squares formula (a+b)⁢(a−b)=a2−b2 open paren a plus b close paren times open paren a minus b close paren equals a squared minus b squared

  2. Assign the values a=3⁢x a equals 3 x and b=4 b equals 4 to fit the formula.

  3. Square the first term: (3⁢x)2=9⁢x2 open paren 3 x close paren squared equals 9 x squared

  4. Square the second term: 42=16 4 squared equals 16

  5. Subtract the squared terms to find the final simplified expression.

Final Answer

(3⁢x+4)⁢(3⁢x−4)=9⁢x2−16 open paren 3 x plus 4 close paren times open paren 3 x minus 4 close paren equals 9 x squared minus 16

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