Simplifying Algebraic Expressions

Show your work for each problem.

1.
Which terms are like terms?
1. a) $2x$ and $2y$
2. b) $3x$ and $5x$
3. c) $4x$ and $4x^2$
4. d) $5$ and $5a$
Answer: $3x$ and $5x$
$3x$ and $5x$ are like terms because both have the variable $x$ to the power of 1. The other pairs have different variables or different exponents.
2.
Simplify: $6x + 3x = \square x$ . What number goes in the box?
Answer: 9
$6x + 3x = 9x$ . We add the coefficients (6 + 3 = 9) and keep the variable $x$ . So the box holds $9$ .
3.
Simplify: $8y - 5y = \square y$ . What number goes in the box?
Answer: 3
$8y - 5y = 3y$ . We subtract the coefficients (8 - 5 = 3) and keep the variable $y$ . So the box holds $3$ .
4.
What is the coefficient in $7a$ ?
1. a) $7a$
2. b) $7$
3. c) $1$
4. d) $a$
Answer: $7$
In $7a$ , the coefficient is $7$ . It's the number that multiplies the variable $a$ .
5.
Simplify: $4x + 2x + 3x$
Answer: 9x
1. Are all three terms like terms? yes
2. Add the coefficients: $4 + 2 + 3 = ?$ 9
3. Which is the simplified expression? $9x$
6.
Simplify: $5a + 3b + 2a = \square a + 3b$ . What number goes in the box?
Answer: 7
$5a + 3b + 2a = 7a + 3b$ . We combine $5a + 2a = 7a$ . The $3b$ stays separate because it has a different variable. So the box holds $7$ .
7.
Simplify: $9x - 4x + 2$
1. a) $13x + 2$
2. b) $5x + 2$
3. c) $5x - 2$
4. d) $7x$
Answer: $5x + 2$
$9x - 4x + 2 = 5x + 2$ . We combine the x terms: $9x - 4x = 5x$ . The constant $2$ is not a like term, so it stays.
8.
Simplify: $3x + 4y - x + 2y$
Answer: 2x + 6y
1. Identify the x terms $3x$ and $-x$
2. Combine the x terms: $3x - x = \square x$ . What number goes in the box? 2
3. Identify the y terms $4y$ and $2y$
4. Combine the y terms: $4y + 2y = \square y$ . What number goes in the box? 6
5. Which is the simplified expression? $2x + 6y$
9.
Simplify: $6x - 6x = \square x$ . What number goes in the box?
Answer: 0
$6x - 6x = 0$ . When we subtract a term from itself, we get zero. So the box holds $0$ ( $0x = 0$ ).
10.
Which expression is already in simplest form?
1. a) $4a - a$
2. b) $5x + 2x$
3. c) $3x + 2y$
4. d) $7b + 3b$
Answer: $3x + 2y$
$3x + 2y$ is already simplified because $x$ and $y$ are different variables and cannot be combined. The other expressions all have like terms that can be combined.
11.
Simplify: $7a + 5 - 3a - 2$
Answer: 4a + 3
1. Identify the variable terms $7a$ and $-3a$
2. Combine the variable terms: $7a - 3a = \square a$ . What number goes in the box? 4
3. Identify the constants $5$ and $-2$
4. Combine the constants: $5 - 2 = ?$ 3
5. Which is the simplified expression? $4a + 3$
12.
Simplify $2x^2 + 5x - x^2 + 3x$ . What is the coefficient of $x^2$ in the simplified expression?
Answer: 1
$x^2$ terms: $2x^2 - x^2 = x^2$ . $x$ terms: $5x + 3x = 8x$ . Answer: $x^2 + 8x$ The coefficient of $x^2$ is $1$ , because $x^2 = 1x^2$ .
13.
Simplify: $4a + 3b - 2a - 5b + 6$
1. a) $6a - 2b + 6$
2. b) $2a + 8b + 6$
3. c) $2a - 2b - 6$
4. d) $2a - 2b + 6$
Answer: $2a - 2b + 6$
$a$ terms: $4a - 2a = 2a$ . $b$ terms: $3b - 5b = -2b$ . Constant: $6$ . Answer: $2a - 2b + 6$
14.
Simplify: $5x^2 + 2x - 3x^2 - 7x + 4$
Answer: 2x^2 - 5x + 4
1. Identify the $x^2$ terms $5x^2$ and $-3x^2$
2. Combine: $5x^2 - 3x^2 = \square x^2$ . What number goes in the box? 2
3. Identify the $x$ terms $2x$ and $-7x$
4. Combine: $2x - 7x = \square x$ . What number goes in the box? -5
5. What is the constant? 4
6. Which is the simplified expression in standard form (highest power first)? $2x^2 - 5x + 4$
15.
Simplify $-2m + 4n - 5m + 3n - 8$ . What is the coefficient of $m$ in the simplified expression?
Answer: -7
$m$ terms: $-2m - 5m = -7m$ . $n$ terms: $4n + 3n = 7n$ . Constant: $-8$ . Answer: $-7m + 7n - 8$ The coefficient of $m$ is $-7$ .
16.
Simplify: $3x^2 + 4xy - 2x^2 + xy - 5$
Answer: x^2 + 5xy - 5
1. Identify the $x^2$ terms $3x^2$ and $-2x^2$
2. Combine: $3x^2 - 2x^2 = \square x^2$ . What number goes in the box? 1
3. Identify the $xy$ terms $4xy$ and $xy$
4. Combine: $4xy + xy = \square xy$ . What number goes in the box? 5
5. What is the constant? -5
6. Which is the simplified expression? $x^2 + 5xy - 5$