Final answer:
The correct rewriting of the expression (2x-7)(x+2)+(3x+7)(x+2) as an equivalent product of two binomials after combining like terms and factoring is (5x)(x+2), but this option is not listed in the provided choices.
Step-by-step explanation:
The expression (2x-7)(x+2)+(3x+7)(x+2) can be rewritten as an equivalent product of two binomials by first combining like terms. To do this, notice that each term is multiplied by (x+2).
First, distribute (x+2) to the terms inside the parentheses:
Combine like terms:
The expression simplifies to 5x2+10x. Factoring out the common factor of 5x results in 5x(x+2), thus the original expression is equivalent to the product of two binomials:
(5x)(x+2)
However, none of the given options matches this result, so the question may contain an error or the options might be wrong. Checking for errors is part of the process of ensuring that your answer is correct and reasonable.