Final answer:
To simplify 2(2x-6)(3x+7), you first distribute the 2, which yields 4x-12, and then multiply this by 3x+7. After expanding and combining like terms, the simplest form of the expression is 12x² - 8x - 84.
Step-by-step explanation:
The question is asking for the simplest way of writing the algebraic expression 2(2x-6)(3x+7). To simplify this expression, we need to expand the terms and eliminate any possible terms to achieve the most simplified form. First, we'll distribute the 2 into the parenthesis which gives us 4x - 12 and then multiply this by (3x+7). Performing the multiplication step-by-step, we have:
- 4x × 3x = 12x²
- 4x × 7 = 28x
- -12 × 3x = -36x
- -12 × 7 = -84
Adding these products together, we get 12x² + 28x - 36x - 84. Combining the like terms (28x and -36x), we obtain:
12x² - 8x - 84
This is the simplest form of the expression, as there are no like terms left to combine and no further factoring is possible. Remember, it is important to check the answer to ensure it is reasonable and matches the original expression's intent.