Question

problem 7
complete the table.
product expression
sum expression
$4x + 8$

Explanation:

Step1: Factor the sum expression

The sum expression is \(4x + 8\). We can factor out the greatest common factor, which is 4.
\(4x+8 = 4(x + 2)\)

Step2: Identify the product expression

From the factoring, the product expression (the factored form) is \(4(x + 2)\) or we can also think of it as a product of two binomials or a monomial and a binomial. If we consider the terms that multiply to give \(4x + 8\), another way is to see that \(4\times x+4\times2\), so the product expression can be written as \(4(x + 2)\) or if we take two factors like \((4)(x + 2)\) or even \((2)(2x + 4)\) but the most simplified factored form is \(4(x + 2)\). Assuming the table has the sum expression \(4x + 8\) and we need the product expression (factored form), the product expression is \(4(x + 2)\) (or if we consider the product of two terms that add up, for example, if we think of the sum as \(4x+8\), the product expression could also be represented as \(4\times x+4\times8\) but that's not factoring. Wait, the sum is \(4x + 8\), so the product expression (the factored form) is \(4(x + 2)\).

Answer:

The product expression corresponding to the sum expression \(4x + 8\) is \(4(x + 2)\) (or other equivalent factored forms like \(2(2x + 4)\) but the standard factored form is \(4(x + 2)\)).