- Simplification means making things easier.
- We can simplify the expressions having various operations.
- Here, we will learn to simplify the expressions having two operations i.e., addition and subtraction.

**For example:**

Simplify: \(8x+16y-2z+3x-7y+5z\)

First, arrange the like terms together.

\(8x+3x+16y-7y-2z+5z\)

Now, take the common variables out.

\(=x(8+3)+y(16-7)+z(-2+5)\)

\(=x(11)+y(9)+z(3)\)

\(=11x+9y+3z\)

A \(x+y-a\)

B \(4x+18y-a\)

C \(18x+4y-a+10\)

D \(x+y+2a\)

- Here, we will learn to simplify the expressions involving addition and multiplication.

**For example:**

Simplify: \(2×a×b×c\;+\;5×a×b×c\;+\;7×a×a×a\)

We will take the common variables out.

\(2×a×b×c\;+\;5×a×b×c\;+\;7×a×a×a\)

\(= 2abc\;+\; 5abc \; +\; 7a^3\)

\(=abc (2+5)+7a^3\)

\(=abc (7)+7a^3\)

\(=7abc+7a^3\)

A \(11e^2f+10f^2e\)

B \(10e^2f+11f^2e\)

C \(7e^2+5f^2\)

D \(2e^2f\)

- Here, we will learn to simplify the expressions involving subtraction and multiplication.

**For example:**

Simplify: \(4×a×b×c-8×a×b×c-3×a×a×b\)

We will take the common variables out from the expression.

\(4×a×b×c-8×a×b×c-3×a×a×b\)

\(=4abc-8abc-3a^2b\)

\(=abc(4-8)-3a^2b\)

\(=abc(-4)-3a^2b\)

\(=-4abc-3a^2b\)

- Here, we will learn to simplify the expressions involving addition and division.

**For example: **

Simplify: \(\dfrac{6p^3q^2+10p^2q}{4q}\)

First, we take the commons out and then divide.

\(\dfrac{6p^3q^2+10p^2q}{4q}\)

\(=\dfrac{ \not{2}p^2\not{q}(3pq+5)}{ \not{4}^2 \not{q}}\)

\(=\dfrac{p^2(3pq+5)}{2}\)

\(=\dfrac{3p^3q+5p^2}{2}\)

- Here, we will learn to simplify the expressions involving subtraction and division.

**For example: **

Simplify: \(\dfrac{3ab^2c-6b^2c^2-3ab^2c^2}{3b^2c}\)

First, we take the commons out and then divide.

\(\dfrac{3ab^2c-6b^2c^2-3ab^2c^2}{3b^2c}\)

\(=\dfrac{\not 3 \not b^2 \not c(a-2c-ac)}{\not 3 \not b^2 \not c}\)

\(=a-2c-ac\)

\(=a-c(2+a)\)

A \(2a^2b^2c\)

B \(abc\)

C \(1\)

D \(-1\)

- Here, we will learn to simplify the expressions involving multiplication and division.

**For example:** \(\dfrac{6×a×a×a×b×b×c}{3×a×b×c}\)

We will cancel out the same variables appearing in both numerator and denominator.

\(\dfrac{ \not{6}^2× \not{a}×a×a×b× \not{b}× \not{c}}{ \not{3}× \not{a}× \not{b}× \not{c}}\)

\(= 2×a×a×b\)

\(=2a^2b\)

A \(\dfrac{2}{pq^2}\)

B \(2pq^2\)

C \(pq^2\)

D \(2\)