What is the product of these binomials? \( (x-6)(x+2)= \) A. \( x^{2}-4 x-12 \) B. \( x^{2}-4 x-4 \) C. \( x^{2}-8 x-4 \) D. \( x^{2}-8 x-12 \)

To find the product of the binomials \( (x-6)(x+2) \), we can use the distributive property, sometimes called the FOIL method (First, Outer, Inner, Last). When we multiply these, we get: 1. First: \( x \cdot x = x^2 \) 2. Outer: \( x \cdot 2 = 2x \) 3. Inner: \( -6 \cdot x = -6x \) 4. Last: \( -6 \cdot 2 = -12 \) Now combining all these results: \( x^2 + 2x - 6x - 12 = x^2 - 4x - 12 \). So, the correct answer is A. \( x^{2}-4 x-12 \)! Now, if you're looking to impress your friends, remember that factoring can be super handy. For instance, from the original product \( (x-6)(x+2) \), if you ever need the expressions back, simply consider finding the roots where each factor equals zero, x=6 and x=-2. Voilà! You've got the solutions! Also, when multiplying binomials, be mindful of sign changes! A small mistake in signs can completely alter your results. Practice by multiplying simple binomials and double-checking your work to ensure you catch any pesky sign errors!