Recognizing Products and Sums; Identifying Factors and Terms
A sum is an expression where the last operation is addition. In a sum, the things being added are called the terms.
As an example, consider the expression $\,a(b+c)\,.$ If numbers are chosen for $\,a\,,$ $\,b\,,$ and $\,c\,,$ then here is the order that computations would be done:
- Add $\,b\,$ and $\,c\,$
- (Pre)-multiply this sum by $\,a\,$
Notice that the last operation done is multiplication. Thus, the expression $\,a(b+c)\,$ is a product. The factors are $\,a\,$ and $\,(b+c)\,.$
As a second example, consider the expression $\,ab + c\,.$ Given numbers $\,a\,,$ $\,b\,,$ and $\,c\,,$ here is the order that computations would be done:
- Multiply $\,a\,$ and $\,b\,$
- Add this result to $\,c\,$
Notice that the last operation done is addition. Thus, the expression $\,ab+c\,$ is a sum. The terms are $\,ab\,$ and $\,c\,.$
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Examples
User input is in bold.
The expression $\,3xy\,$ is a product.
The factors are: 3, x, y
Note: The factors must be listed in order from left to right, and must be separated by commas.
The expression $\,-4x(x+2)\,$ is a product.
The factors are: -4, x, x+2
Note: Do not use parentheses when listing factors. (That is, don't put the x+2 inside parentheses.)
The expression $\,5x - y + 1\,$ is a sum.
The terms are: 5x, -y, 1
Note: The terms must be listed in order from left to right, and must be separated by commas. Remember that a term includes its sign.
The expression $\,x^2 + 2y^3 - 7\,$ is a sum.
The terms are: x^2, 2y^3, -7
Note: Exponents are input using the ‘ ^ ’ key.
