Final answer:
The multiplication of (a + b)(a - b) results in the difference of squares formula, a2 - b2. This algebraic identity is also applicable to complex numbers where multiplying by a complex conjugate eliminates the imaginary parts, resulting in a real number, a2 + b2.
Step-by-step explanation:
The question refers to the multiplication of two binomials, specifically (a + b)(a − b), which is a fundamental concept in algebra known as the difference of squares. The result of multiplying these two binomials is indeed a2 − b2. When dealing with complex numbers, such as A = a + ib, where i is the imaginary unit and a and b are real numbers, multiplying a complex number by its conjugate (A * A* = (a + ib)(a − ib)) results in a real number (a2 + b2), as the imaginary parts cancel out.
To 'undo' or 'invert' the square, for example, to solve for one side of a right triangle using the Pythagorean theorem, one would take the square root of both sides of the equation a2 + b2 = c2, resulting in a on one side. This concept is essential in solving many algebraic problems involving squares and square roots.