Terms with identical variable structure

Question 1

What are “like terms?”

Answer 1

In the combination of terms, the like terms are identical variable parts (including exponents). You manipulate expressions w/these like terms by adding or subtracting their coefficients.

Question 2

What do you call (3y – 5) ?

Answer 2

It’s an expression consisting of two terms. (3y – 5) is a binomial expression (or simply, a binomial), not a single term.

Question 3

When combining like terms with negative coefficients & distribution, how do you solve these problems, such as the problem in the photo?

Answer 3

identify the multiplicative factor or scalar factor: When referring to a number multiplying an entire expression or quantity. Then, see the photo…

Question 4

When writing expressions, why do we list the terms with coefficients first, such as 17k-25?

Answer 4

Emphasize the variable part of the expression, which is often the focus in algebraic manipulation. It’s more of a human thing, not a math thing, to organize it in this way. It’s standard convention.

Question 5

How do we properly describe the combination of +1-36?

Answer 5

It’s a combination of numeric terms.

Question 6

Answer 6

combining rational coefficients: You can factor the shared variable outside the parentheses because of the distributive property, which allows you to combine the numeric coefficients of identical variable terms. This is a fundamental property of arithmetic and algebra.