Combining Like Terms

Show your work for each problem.

1.
Simplify: $5x + 3x$
1. a) $8x$
2. b) $8x^2$
3. c) $8$
4. d) $15x$
Answer: $8x$
$5x + 3x = 8x$ . We add the coefficients $5 + 3 = 8$ and keep the variable $x$ .
2.
$7y - 2y = \square y$ . What number goes in the box?
Answer: 5
$7y - 2y = 5y$ . We subtract the coefficients $7 - 2 = 5$ and keep the variable $y$ .
3.
Which pair consists of like terms?
1. a) $3x$ and $3y$
2. b) $7$ and $7x$
3. c) $2x$ and $5x^2$
4. d) $4x$ and $9x$
Answer: $4x$ and $9x$
$4x$ and $9x$ are like terms because they both have the variable $x$ with the same exponent (1).
4.
Simplify $x + 4x$ . What is the coefficient of $x$ in the result?
Answer: 5
$x + 4x = 1x + 4x = 5x$ . Remember that $x$ has an invisible coefficient of 1.
5.
Simplify: $6a + 2a$
Answer: 8a
1. Are $6a$ and $2a$ like terms? yes
2. What is $6 + 2$ ? 8
3. What is the simplified expression? 8a
6.
Simplify $4x + 3y + 2x$ . What is the coefficient of $x$ in the result?
Answer: 6
$4x + 3y + 2x = (4x + 2x) + 3y = 6x + 3y$ . Only the $x$ terms can be combined.
7.
Simplify: $3a + 5b + 2a - b$
1. a) $9ab$
2. b) $5a - 4b$
3. c) $5a + 4b$
4. d) $5a + 6b$
Answer: $5a + 4b$
$3a + 5b + 2a - b = (3a + 2a) + (5b - b) = 5a + 4b$ . Remember $-b = -1b$ .
8.
Simplify: $5x + 3 + 2x - 7$
Answer: 7x - 4
1. Identify the x terms. What are they? 5x and 2x
2. Combine the x terms: $5x + 2x = ?$ 7x
3. Identify the constants. What are they? 3 and -7
4. Combine the constants: $3 + (-7) = ?$ -4
5. Write the final simplified expression 7x - 4
9.
$8m - 3m + m = \square m$ . What number goes in the box?
Answer: 6
$8m - 3m + m = 8m - 3m + 1m = (8 - 3 + 1)m = 6m$
10.
Simplify: $2x + 5y - x + 3y$
Answer: x + 8y
1. Combine the x terms: $2x - x = ?$ x
2. Combine the y terms: $5y + 3y = ?$ 8y
3. Write the final expression x + 8y
11.
Which expression is fully simplified?
1. a) $4x + 5x$
2. b) $3x + 2y$
3. c) $2a + 3a + b$
4. d) $6m - 2m$
Answer: $3x + 2y$
$3x + 2y$ is fully simplified because $x$ and $y$ are unlike terms. The other expressions still have like terms to combine.
12.
Simplify $4x^2 + 3x + 2x^2 - x$ . What is the coefficient of $x$ (not of $x^2$ ) in the result?
Answer: 2
$4x^2 + 3x + 2x^2 - x = (4x^2 + 2x^2) + (3x - x) = 6x^2 + 2x$ . Note: $x^2$ and $x$ have different exponents, so they cannot be combined.
13.
Simplify: $3a + 2b - 5 + 4a - b + 8$
Answer: 7a + b + 3
1. Combine the a terms: $3a + 4a = ?$ 7a
2. Combine the b terms: $2b - b = ?$ b
3. Combine the constants: $-5 + 8 = ?$ 3
4. Write the final expression 7a + b + 3
14.
Simplify: $-2x + 5 - 3x - 8$
1. a) $-x - 3$
2. b) $-5x + 3$
3. c) $5x - 3$
4. d) $-5x - 3$
Answer: $-5x - 3$
$-2x + 5 - 3x - 8 = (-2x - 3x) + (5 - 8) = -5x + (-3) = -5x - 3$
15.
Simplify: $5x^2 - 2x + 3x^2 + 4x - 7$
1. a) $8x^2 + 2x - 7$
2. b) $10x^3 - 7$
3. c) $8x^2 - 6x - 7$
4. d) $8x^4 + 2x - 7$
Answer: $8x^2 + 2x - 7$
$5x^2 - 2x + 3x^2 + 4x - 7 = (5x^2 + 3x^2) + (-2x + 4x) + (-7) = 8x^2 + 2x - 7$
16.
Simplify: $2(x + 3) + 4x$
Answer: 6x + 6
1. First, expand $2(x + 3)$ : 2x + 6
2. Combine the $x$ terms in $2x + 6 + 4x$ : $2x + 4x = \square x$ . What number goes in the box? 6
3. Write the simplified expression: 6x + 6