Free custom combining like terms worksheet templates - Free Printable

To simplify the given expressions by combining like terms, we need to group and add or subtract terms that have the same variables raised to the same powers. Let's solve each expression step by step.

---

a) \( 3x + 2y - 5x + 4y \)

1. Group the \( x \)-terms: \( 3x - 5x \)
\[
3x - 5x = -2x
\]
2. Group the \( y \)-terms: \( 2y + 4y \)
\[
2y + 4y = 6y
\]
3. Combine the results:
\[
-2x + 6y
\]

Answer:
\[
\boxed{-2x + 6y}
\]

---

b) \( 4x - 3y + y - 2x \)

1. Group the \( x \)-terms: \( 4x - 2x \)
\[
4x - 2x = 2x
\]
2. Group the \( y \)-terms: \( -3y + y \)
\[
-3y + y = -2y
\]
3. Combine the results:
\[
2x - 2y
\]

Answer:
\[
\boxed{2x - 2y}
\]

---

c) \( 2x + 3y - 4x - 2y \)

1. Group the \( x \)-terms: \( 2x - 4x \)
\[
2x - 4x = -2x
\]
2. Group the \( y \)-terms: \( 3y - 2y \)
\[
3y - 2y = y
\]
3. Combine the results:
\[
-2x + y
\]

Answer:
\[
\boxed{-2x + y}
\]

---

d) \( 6y + 2x - 3 - 2y + 4 \)

1. Group the \( x \)-terms: \( 2x \) (no other \( x \)-terms)
\[
2x
\]
2. Group the \( y \)-terms: \( 6y - 2y \)
\[
6y - 2y = 4y
\]
3. Group the constant terms: \( -3 + 4 \)
\[
-3 + 4 = 1
\]
4. Combine the results:
\[
2x + 4y + 1
\]

Answer:
\[
\boxed{2x + 4y + 1}
\]

---

e) \( 5 - 3y + 7x - 3 + 2y \)

1. Group the \( x \)-terms: \( 7x \) (no other \( x \)-terms)
\[
7x
\]
2. Group the \( y \)-terms: \( -3y + 2y \)
\[
-3y + 2y = -y
\]
3. Group the constant terms: \( 5 - 3 \)
\[
5 - 3 = 2
\]
4. Combine the results:
\[
7x - y + 2
\]

Answer:
\[
\boxed{7x - y + 2}
\]

---

f) \( 4xy + 2y - 5xy - 6y \)

1. Group the \( xy \)-terms: \( 4xy - 5xy \)
\[
4xy - 5xy = -xy
\]
2. Group the \( y \)-terms: \( 2y - 6y \)
\[
2y - 6y = -4y
\]
3. Combine the results:
\[
-xy - 4y
\]

Answer:
\[
\boxed{-xy - 4y}
\]

---

g) \( 7 - 5y + 2xy + 3 - y \)

1. Group the \( xy \)-terms: \( 2xy \) (no other \( xy \)-terms)
\[
2xy
\]
2. Group the \( y \)-terms: \( -5y - y \)
\[
-5y - y = -6y
\]
3. Group the constant terms: \( 7 + 3 \)
\[
7 + 3 = 10
\]
4. Combine the results:
\[
2xy - 6y + 10
\]

Answer:
\[
\boxed{2xy - 6y + 10}
\]

---

h) \( 3y - 3xy - y - 7xy \)

1. Group the \( y \)-terms: \( 3y - y \)
\[
3y - y = 2y
\]
2. Group the \( xy \)-terms: \( -3xy - 7xy \)
\[
-3xy - 7xy = -10xy
\]
3. Combine the results:
\[
2y - 10xy
\]

Answer:
\[
\boxed{2y - 10xy}
\]

---

i) \( 2x^2 + 3x + 6x^2 - 2x \)

1. Group the \( x^2 \)-terms: \( 2x^2 + 6x^2 \)
\[
2x^2 + 6x^2 = 8x^2
\]
2. Group the \( x \)-terms: \( 3x - 2x \)
\[
3x - 2x = x
\]
3. Combine the results:
\[
8x^2 + x
\]

Answer:
\[
\boxed{8x^2 + x}
\]

---

j) \( 7y^2 - 6y + 3y - 2y^2 \)

1. Group the \( y^2 \)-terms: \( 7y^2 - 2y^2 \)
\[
7y^2 - 2y^2 = 5y^2
\]
2. Group the \( y \)-terms: \( -6y + 3y \)
\[
-6y + 3y = -3y
\]
3. Combine the results:
\[
5y^2 - 3y
\]

Answer:
\[
\boxed{5y^2 - 3y}
\]

---

k) \( 2xy^2 - xy + 4xy^2 \)

1. Group the \( xy^2 \)-terms: \( 2xy^2 + 4xy^2 \)
\[
2xy^2 + 4xy^2 = 6xy^2
\]
2. Group the \( xy \)-terms: \( -xy \) (no other \( xy \)-terms)
\[
-xy
\]
3. Combine the results:
\[
6xy^2 - xy
\]

Answer:
\[
\boxed{6xy^2 - xy}
\]

---

Final Answers:

\[
\boxed{
\begin{aligned}
&\text{a) } -2x + 6y \\
&\text{b) } 2x - 2y \\
&\text{c) } -2x + y \\
&\text{d) } 2x + 4y + 1 \\
&\text{e) } 7x - y + 2 \\
&\text{f) } -xy - 4y \\
&\text{g) } 2xy - 6y + 10 \\
&\text{h) } 2y - 10xy \\
&\text{i) } 8x^2 + x \\
&\text{j) } 5y^2 - 3y \\
&\text{k) } 6xy^2 - xy
\end{aligned}
}
\]