134r. Review Like Terms and Simplifying Expressions

Learning Intentions

To understand that like terms contain exactly the same pronumerals, possibly in a different order
decide if two terms are like terms
combine like terms to simplify expressions

Know that a term is a part of an expression separated by $+$ or $-$ signs
Know that a coefficient is the number multiplying the pronumeral part of a term
Understand that pronumerals stand for numbers
Be able to identify the pronumerals in a term
Know that multiplication can be written without the $\times$ sign, for example $3 a b$
Understand that the order of pronumerals in a product does not change the term, for example $a b = b a$

State whether each pair of terms is like terms:
a) $3 x$ and $- 5 x$
b) $4 a b$ and $7 b a$
c) $2 a$ and $2 b$

State whether each pair of terms is like terms:
a) $6 m^{2}$ and $- 3 m^{2}$
b) $5 x y$ and $8 x$
c) $9 p q$ and $2 q p$

Combine like terms to simplify:
a) $3 x + 5 x$
b) $7 a - 2 a$
c) $4 m + m$

Combine like terms to simplify:
a) $6 a b + 3 b a$
b) $9 y - 4 y + 2 y$
c) $8 p + 5 - 3 p$

Simplify each expression by combining like terms:
a) $4 x + 2 y + 3 x$
b) $7 a b - 2 b a + 5$
c) $6 m - 4 n + 3 m - 2$

Simplify each expression by combining like terms:
a) $5 x + 2 - 3 x + 7$
b) $4 p q + 6 q p - 5 p q$
c) $3 a + 2 b - a + 5 b$

State whether each pair of terms is like terms:
a) $8 x$ and $3 x$
b) $5 c d$ and $2 d c$
c) $7 m$ and $7 n$

State whether each pair of terms is like terms:
a) $4 t^{2}$ and $9 t^{2}$
b) $6 r s$ and $6 r$
c) $3 u v$ and $5 v u$

Combine like terms to simplify:
a) $2 x + 6 x$
b) $9 a - 4 a$
c) $5 m + 2 m$

Combine like terms to simplify:
a) $7 a b + 4 b a$
b) $10 y - 3 y + y$
c) $6 p + 8 - 2 p$

Simplify each expression by combining like terms:
a) $5 x + y + 4 x$
b) $8 a b - 3 b a + 6$
c) $9 m - 2 n + m - 4$

Simplify each expression by combining like terms:
a) $7 x + 1 - 2 x + 9$
b) $3 p q + 5 q p - p q$
c) $4 a + 3 b - 2 a + b$

State whether each pair of terms is like terms:
a) $3 x$ and $9 x$
b) $4 a b$ and $6 b a$
c) $5 m$ and $5 n$
d) $2 p^{2}$ and $7 p^{2}$
State whether each pair of terms is like terms:
a) $8 x y$ and $3 y x$
b) $6 a$ and $6 a b$
c) $7 r^{2}$ and $2 r$
d) $9 c d$ and $4 d c$
Combine like terms to simplify:
a) $4 x + 3 x$
b) $8 y - 5 y$
c) $6 a + a$
d) $9 m - 2 m$
Combine like terms to simplify:
a) $5 a b + 2 b a$
b) $7 p q - 3 q p$
c) $10 x + 4 - 6 x$
d) $3 y + 8 + 2 y + 1$
Simplify each expression:
a) $3 x + 2 y + 4 x$
b) $6 a - 2 b + 5 a$
c) $7 m n + 3 n m - 4$
d) $8 p + 6 - 5 p + 2$
Simplify each expression:
a) $9 x - 4 x + 2$
b) $5 a b + 7 - 2 b a + 1$
c) $4 m + 3 n + 2 m - n$
d) $6 r + 5 s - 2 r + 4 s$
Decide which terms are like terms, then simplify:
a) $2 x + 3 y + 5 x$
b) $4 a b + 6 b a - 2 c$
c) $7 m - 3 n + 2 m - n$
d) $8 p q + p q + 4 - 1$
Fill in the blank to make like terms:
a) $3 x + ◻ x = 11 x$
b) $5 a b + ◻ b a = 12 a b$
c) $9 m - ◻ m = 4 m$
d) $2 y + 7 + 3 y + ◻ = 5 y + 10$

Explain why $4 a b$ and $9 b a$ are like terms.
A student says that $3 x$ and $3 x^{2}$ are like terms because both contain $x$ . Explain the mistake.
Noah says that $2 a b$ and $2 a$ are like terms because both contain $a$ . Is he correct? Explain.
Explain why only like terms can be combined when simplifying an expression.
A student simplifies $3 x + 2 y + 4 x$ to $9 x y$ . Describe the error.

A shop sells pens for $p$ dollars each and notebooks for $n$ dollars each. A customer buys $3$ pens, $2$ notebooks and then $4$ more pens. Write and simplify the total cost.
A rectangle has side lengths $x + 2$ and $x + 5$ . Write an expression for the sum of the two lengths and simplify it.
A student scores $a$ points in round one, $b$ points in round two, and then $3 a$ more points in round three. Write and simplify the total score.
A bag contains $5 r$ red counters, $2 b$ blue counters and another $3 r$ red counters. Write and simplify the total number of counters in terms of $r$ and $b$ .
A builder uses $6 m n$ tiles in one section, $4 n m$ tiles in another section, and removes $3 m n$ tiles. Write and simplify the final number of tiles.
A pattern has $2 x + 3$ squares in one row and $5 x + 4$ squares in another row. Write and simplify the total number of squares.

Students may think terms are like terms just because they share one pronumeral
Students may think coefficients must be the same for terms to be like terms
Students may not recognise that $a b$ and $b a$ represent the same pronumeral part
Students may think $x$ and $x^{2}$ are like terms
Students may combine unlike terms into a single product, such as turning $3 x + 2 y$ into $5 x y$
Students may forget to include the sign of a term when combining like terms
Students may combine constant terms with variable terms incorrectly
Students may overlook that a term with no written coefficient has coefficient $1$