Final answer:
The word phrase 'eight times the sum of 7x and seven' translates to the algebraic expression 8(7x + 7). We consider the sum inside the parentheses first, then multiply by eight. Simplification, in this case, does not reduce the terms further.
Step-by-step explanation:
To translate the word phrase 'eight times the sum of 7x and seven' into an algebraic expression, we start by interpreting the phrase 'the sum of 7x and seven' which means we add 7x and 7 together. This gives us the expression (7x + 7). Next, we multiply this sum by eight; therefore, the entire expression becomes 8(7x + 7).
When simplifying, there are no like terms within the parentheses, so we cannot eliminate terms further within the sum. If we decide to apply the distributive property to remove the parentheses, it would then become 56x + 56; however, simplification doesn't affect the value of the expression. Always check the answer to make sure it makes sense given the original phrase, which in this case, it does.