Question

How many terms are in this expression? 10 + 8x - 3(y-5) + 15t

A. 4 terms
B. 5 terms
C. 6 terms
D. 7 terms

Answer 1

The expression 10 + 8x - 3(y-5) + 15t can be simplified to include 4 terms: a single constant term (25 after combining like terms), and one linear term in each of the variables x, y, and t.

Step-by-step explanation:

The student has asked about the number of terms in the expression 10 + 8x - 3(y-5) + 15t. A term in algebra is a single mathematical expression. It can be a number, a variable, or a number multiplied by a variable or variables. In this case, the expression can be simplified to see all the terms clearly.

First, let's look at the expression as is:

1. 10 is the first term.
2. 8x is the second term.
3. The third term is a bit more complex: -3(y-5) should be expanded before we can count the terms inside the parentheses.
4. +15t is another term.

Once we distribute the -3 into the parentheses, we get -3y + 15. So we actually have two more terms from inside the parentheses. This gives us:

1. 10 (constant term)
2. + 8x (linear term in x)
3. - 3y (linear term in y)
4. + 15 (constant term from the distribution, which adds to the first constant term)
5. + 15t (linear term in t)

Now that we have expanded the expression, we can see that 15 from the distribution gets added to 10, resulting in a single constant term of 25. Thus, the actual terms in the expression are:

• 25 (constant term)
• 8x (linear term in x)
• -3y (linear term in y)
• 15t (linear term in t)

So, the expression 10 + 8x - 3(y-5) + 15t actually has 4 terms.