The product of the binomials (x-6) and (x + 2) is obtained using the FOIL method. After multiplying the terms and simplifying, the product is x² - 4x - 12, which is option (A).
Step-by-step explanation:
To find the product of the binomials (x-6) and (x + 2), we apply the distributive property, also known as the FOIL method for binomials, which stands for First, Outside, Inside, Last:
First: Multiply the first terms in each binomial: x × x = x².
Outside: Multiply the outer terms: x × 2 = 2x.
Inside: Multiply the inner terms: -6 × x = -6x.
Last: Multiply the last terms in each binomial: -6 × 2 = -12.
Now, combine these products:
x² + 2x - 6x - 12
Simplify by combining like terms:
x² + (2x - 6x) - 12 = x² - 4x - 12
Therefore, the product of the binomials (x-6) and (x + 2) is x² - 4x - 12, which corresponds to option (A).