036. Like Terms and Simplifying Expressions

Learning Intentions

Understand that a term is a part of an expression separated by addition or subtraction
Know that a coefficient is the numerical part of a term such as the $3$ in $3 x$
Understand that a variable is a letter representing a number
Recognise that a constant term has no variable, such as $5$
Be able to identify the variable part of a term, such as $x$ in $4 x$
Know that addition and subtraction determine whether terms are separate
Understand that only terms with the same variable part can be combined
Be able to substitute simple values into expressions if needed to check reasoning

a) Explain what like terms are.
b) State which terms are like in the expression $3 x + 5 + 2 x - 4$ .
c) State which terms are not like.

Identify the like terms in each expression:
a) $4 a + 7 + 2 a - 3$
b) $5 m + 2 n + 3 m$
c) $6 p - 4 + p + 9$

Simplify by combining like terms:
a) $3 x + 2 x$
b) $7 y - 4 y$
c) $5 a + 3 - 2 a$

Simplify by combining like terms:
a) $4 m + 6 + 3 m - 2$
b) $8 p - 5 + 2 p + 7$
c) $9 q - 4 q + 1$

Simplify each expression:
a) $6 x + 2 y + 3 x - y$
b) $7 a - 2 + 5 a + 8$
c) $10 n - 3 n + 4 - 1$

For each expression:
a) identify the like terms
b) combine the like terms
c) write the simplified expression
For $5 x + 3 y + 2 x - y + 4$

a) Explain what like terms are.
b) State which terms are like in the expression $4 x + 6 + x - 2$ .
c) State which terms are not like.

Identify the like terms in each expression:
a) $3 a + 8 + 5 a - 1$
b) $6 m + n + 4 m$
c) $7 p - 3 + 2 p + 5$

Simplify by combining like terms:
a) $4 x + 3 x$
b) $9 y - 5 y$
c) $6 a + 2 - 4 a$

Simplify by combining like terms:
a) $5 m + 4 + 2 m - 1$
b) $9 p - 6 + p + 3$
c) $8 q - 3 q + 2$

Simplify each expression:
a) $7 x + y + 2 x - 3 y$
b) $6 a - 4 + 3 a + 9$
c) $11 n - 5 n + 6 - 2$

For each expression:
a) identify the like terms
b) combine the like terms
c) write the simplified expression
For $4 x + 2 y + 3 x - y + 5$

State which pairs are like terms:
a) $3 x$ and $5 x$
b) $2 a$ and $2 b$
c) $7$ and $- 4$
State which pairs are like terms:
a) $4 m$ and $m$
b) $3 p$ and $3 p^{2}$
c) $6 y$ and $2 y$
Identify all like terms in each expression:
a) $2 x + 5 + 7 x$
b) $3 a + 4 b + 2 a$
c) $6 m - 1 + m + 8$
Identify all like terms in each expression:
a) $5 p + 2 q + 4 p - q$
b) $8 r + 3 - 2 r + 6$
c) $7 n + n - 5 + 9$
Simplify by combining like terms:
a) $2 x + 6 x$
b) $9 y - 2 y$
c) $4 a + 3 a$
Simplify by combining like terms:
a) $7 m - 3 m$
b) $10 p + p$
c) $12 q - 5 q$
Simplify each expression:
a) $3 x + 2 + 5 x$
b) $6 a - 1 + 2 a$
c) $8 n + 4 - 3 n$
Simplify each expression:
a) $4 y + 7 + y - 2$
b) $9 p - 5 + 2 p + 1$
c) $5 m + 3 n + 2 m$
Simplify each expression:
a) $7 x + 2 y + 3 x - y$
b) $4 a + 8 - a + 2$
c) $11 k - 4 k + 6 - 3$
Simplify each expression:
a) $6 m + 5 n + 3 m - 2 n$
b) $8 p - 4 + 2 p + 9$
c) $9 r - r + 7 - 5$

Explain why $3 x$ and $5 x$ are like terms but $3 x$ and $3 y$ are not like terms.
A student says $4 a + 2 b = 6 a b$ . Explain the mistake.
Explain why constant terms can be combined with other constant terms.
A student simplifies $5 x + 2 + 3 x$ to $8 x + 2 x$ . Explain why this is incorrect.

A student collects expression cards labelled $3 x$ , $5 x$ , $2$ , $- 1$ , and $4 y$ . Combine the like terms to make a simplified expression.
A shop has a cost expression of $4 n + 3 + 2 n + 5$ , where $n$ is the number of notebooks. Simplify the expression for the total cost.
A taxi fare is modelled by $6 k + 4 + 2 k - 1$ , where $k$ is the number of kilometres. Simplify the expression.
A pattern has total tiles given by $5 t + 2 + 3 t + 7$ , where $t$ is the step number. Simplify the expression and state the coefficient of $t$ .

Students may think terms are like terms just because they have the same coefficient
Students may think $x$ -terms and $y$ -terms can be combined because both contain letters
Students may combine unlike terms, for example writing $3 x + 2 y = 5 x y$
Students may forget that constant terms are like terms with each other
Students may split a term incorrectly, treating $3 x$ as two separate terms
Students may ignore the sign in front of a term when combining like terms
Students may think $x$ and $x^{2}$ are like terms even though their variable parts are different
Students may combine some like terms correctly but leave others uncombined in the same expression