Question

Sam says that he knows a clever set of steps to rewrite the expression

(x + 3)(3x+ 8) - 3x(x + 3)
as a sum of two terms where the steps do not involve multiplying the linear factors first and then
collecting like terms. Rewrite the expression as a sum of two terms (where one term is a number and the
other is a product of a coefficient and variable) using Sam’s steps if you can.

Answer 1

8x +24

Explanation:

The easiest way to rewrite the expression is to find a common factor in both terms of the equation. In this case, (x+3) is the common factor and, therefore, the equation can be rewritten and solved as follows:

`(x+3)*[(3x+8)-3x]\\(x+3)*8\\8x +24`

The method presented above successfully finds an expression comprised of the sum of two terms through Sam's steps.