
In order to understand the basic algebra lessons well, we invite you to complete a set of exercises of varying degrees of difficulty. This list of exercises will enable you to fine tune a lot of math rules and will develop the way you think and approach problem solving. We apologize for the lack of exercises because the site is still under construction.

basic algebra (pre-algebra) exercises with solution. You can find here all you need to understand the basics of college maths.

Pre Algebra

# Exercises on Simplifying algebraic expressions by Combining Like Terms
<Parag>This is a set of solved exercises on simplifying algebraic expressions by combining like terms. All you have to do is try to solve these exercises and compare your answers with the answers suggested by us.</Parag>
<Parag>We invite you to visit Lesson <Link to="../../lessons/basic-algebra/simplifying-algebraic-expressions-by-combining-like-terms">Simplifying algebraic expressions by Combining Like Terms
</Link> before starting to do the exercises.</Parag>
<Card numexer="1">
Simplify the follwing expressions by combining like terms::

1. <Tex>\quad A=3x+7x</Tex>
2. <Tex>\quad B=-6k+5k</Tex>
3. <Tex>\quad C=-4x-10x</Tex>
4. <Tex>\quad D=-n+4-9-5n</Tex>
5. <Tex>\quad E=4x-5y+x+8y</Tex>
6. <Tex>\quad F=11x-13x+y</Tex>
7. <Tex>\quad G=5y^2-y^2</Tex>
8. <Tex>\quad H=12x^2+24x+40x^2+30x</Tex>
9. <Tex>\quad I=4x-3y+2x+y-x+2y</Tex>
10. <Tex>\quad J=12x-xy-3x^2+8y+10xy+3x^2-7x</Tex>
</Card>

<Solution>

1. <Tex>\quad 3x</Tex> and <Tex>7x</Tex> are like terms. So, we can combine them: 

<Tex block>
\begin{align*}
A&=3x+7x \\\
&=(3+7)x \\\
&=10x
\end{align*}
</Tex>

2. <Tex>\quad -6k</Tex> and <Tex>5k</Tex> are like terms. So, we can combine them: 

<Tex block>
\begin{align*}
B&=-6k+5k \\\
&=(-6+5)k \\\
&=-1k \\\
&=-k
\end{align*}
</Tex>

3. <Tex>\quad -4x</Tex> and <Tex>-10x</Tex> are like terms. So, we can combine them: 

<Tex block>
\begin{align*}
C&=-4x-10x \\\
&=(-4-10)x \\\
&=-14x
\end{align*}
</Tex>

4. <Tex>\quad -n</Tex> and <Tex>-5n</Tex> are like terms. So, we can combine them: 

<Tex block>
\begin{align*}
D&=-n+4-9-5n \\\
&=(-1-5)n+(4-9) \\\
&=-6n-5
\end{align*}
</Tex>

5. <Tex>\quad 4x</Tex> and <Tex>x</Tex> are like terms. So, we can combine them. Also, <Tex>-5y</Tex> and <Tex>8y</Tex> are like terms and we can combine them: 

<Tex block>
\begin{align*}
E&=4x-5y+x+8y \\\
&=(4+1)x+(-5+8)y \\\
&=5x+3y
\end{align*}
</Tex>

6. <Tex>\quad 11x</Tex> and <Tex>-13x</Tex> are like terms. So, we can combine them: 

<Tex block>
\begin{align*}
F&=11x-13x+y \\\
&=(11-13)x+y \\\
&=-2x+y
\end{align*}
</Tex>

7. <Tex>\quad 5y^2</Tex> and <Tex>-y^2</Tex> are like terms. So, we can combine them: 

<Tex block>
\begin{align*}
G&=5y^2-y^2 \\\
&=(5-1)y^2 \\\
&=4y^2
\end{align*}
</Tex>

8. <Tex>\quad 12x^2</Tex> and <Tex>40x^2</Tex> are like terms. So, we can combine them. Also, <Tex>24x</Tex> and <Tex>30x</Tex> are like terms and we can combine them: 

<Tex block>
\begin{align*}
H&=12x^2+24x+40x^2+30x \\\
&=(12+40)x^2+(24+30)x \\\
&=52x^2+54x
\end{align*}
</Tex>

9. We can combine the term <Tex>4x</Tex> with the terms <Tex>2x</Tex> and <Tex>-x</Tex>, and combine the term <Tex>-3y</Tex> with the terms <Tex>y</Tex> and <Tex>2y</Tex>:

<Tex block>
\begin{align*}
I&=4x-3y+2x+y-x+2y \\\
&=(4+2-1)x+(-3+1+2)y \\\
&=5x+0y \\\
&=5x
\end{align*}
</Tex>

10. <Tex>\quad 12x</Tex> and <Tex>-7x</Tex> are like terms, 
<Tex>-xy</Tex> and <Tex>10xy</Tex> are like terms, 
<Tex>-3x^2</Tex> and <Tex>3x^2</Tex> are like terms and additive inverse. So,
<Tex block>
\begin{align*}
J&=12x-xy-3x^2+8y+10xy+3x^2-7x \\\
&=(12-7)x+(-1+10)xy+(-3+3)x^2+8y \\\
&=5x+9xy+0x^2+8y \\\
&=5x+9xy+8y
\end{align*}
</Tex>
</Solution>

-----------

<Card numexer="2">
Remove the symbols of grouping and simplify the resulting expressions by combining like terms:

1. <Tex>\quad K=(x+3y-z)-(2y-x+3z)+(4z-3x+2y)</Tex>
2. <Tex>\quad L=3(x^2-2yz+y^2)-4(x^2-y^2-3yz)+x^2+y^2</Tex>
3. <Tex>\quad M=3x+4y+3[x-2(y-x)-y]</Tex>
4. <Tex>\quad N=3-[2x-[1-(x+y)]+(x-2y)]</Tex>
</Card>

<Solution>
 <Parag>Remember this rules:</Parag>
 <Note>

1. If a <Tex>(+)</Tex> sign precedes a symbol of grouping, this symbol of grouping may be removed without affecting the terms contained.
2. If a <Tex>(-)</Tex> sign precedes a symbol of grouping, this symbol of grouping may be removed if each sign of the terms contained is changed.
3. If more than one symbol of grouping is present, the inner ones are to be removed first.
</Note>

1. Removing the symbols of grouping and simplifying the expresseion <Tex>k</Tex>:
 <Tex block>
\begin{align*}
K&=(x+3y-z)-(2y-x+3z)+(4z-3x+2y) \\\
&=x+3y-z-2y+x-3z+4z-3x+2y \\\
&=(1+1-3)x+(3-2+2)y+(-1-3+4)z \\\
&=-x+3y+0z \\\
&=-x+3y
\end{align*}
 </Tex>

2. Removing the symbols of grouping, applying the distributive properties and simplifying the expresseion <Tex>L</Tex>:
 <Tex block>
\begin{align*}
L&=3(x^2-2yz+y^2)-4(x^2-y^2-3yz)+x^2+y^2 \\\
&=3x^2-6yz+3y^2-4x^2+4y^2+12yz+x^2+y^2 \\\
&=(3-4+1)x^2+(3+4+1)y^2+(-6+12)yz \\\
&=0x^2+8y^2+6yz \\\
&=-8y^2+6yz
\end{align*}
 </Tex>

3. Removing the symbols of grouping, applying the distributive properties and simplifying the expresseion <Tex>M</Tex>:
 <Tex block>
\begin{align*}
M&=3x+4y+3[x-2(y-x)-y] \\\
&=3x+4y+3[x-2y+2x-y] \\\
&=3x+4y+3x-6y+6x-3y \\\
&=(3+3+6)x+(4-6-3)y \\\
&=12x-5x
\end{align*}
 </Tex>

4. Removing the symbols of grouping, applying the distributive properties and simplifying the expresseion <Tex>N</Tex>:
 <Tex block>
\begin{align*}
N&=3-[2x-[1-(x+y)]+(x-2y)] \\\
&=3-[2x-[1-x-y]+x-2y] \\\
&=3-[2x-1+x+y+x-2y] \\\
&=3-2x+1-x-y-x+2y \\\
&=4+(-2-1-1)x+(-1+2)y \\\
&=4-4x+y
\end{align*}
 </Tex>
</Solution>

Some exercises with solution about simplifying algebraic expressions by combining like terms method.

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