Solving the Equation (x+3)(x3) = 27
This article will guide you through solving the equation (x+3)(x3) = 27.
Understanding the Equation
The equation (x+3)(x3) = 27 involves a product of two binomials. This pattern is a special case in algebra known as the "difference of squares" pattern.
The Difference of Squares Pattern:
(a + b)(a  b) = a²  b²
Solving the Equation

Expand the left side: Using the difference of squares pattern, we can expand the left side of the equation: (x + 3)(x  3) = x²  3² (x + 3)(x  3) = x²  9

Rewrite the equation: Now our equation becomes: x²  9 = 27

Isolate the x² term: Add 9 to both sides of the equation: x² = 27 + 9 x² = 36

Solve for x: Take the square root of both sides: x = ±√36 x = ±6
Solutions
Therefore, the solutions to the equation (x+3)(x3) = 27 are:
 x = 6
 x = 6
Verification
We can verify these solutions by plugging them back into the original equation:
 For x = 6: (6 + 3)(6  3) = (9)(3) = 27
 For x = 6: (6 + 3)(6  3) = (3)(9) = 27
Both solutions satisfy the original equation.