- 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: \(5a+6a-7a+8a\)

Here, we know that \(5a,\,6a,\,-7a\) and \(8a\) are all like terms.

We can simplify the expression by taking the common variable out.

Thus, \(5a+6a-7a+8a\)

\(= a(5+6-7+8)\)

\( = a (19-7)\)

\( = a (12)\)

\( = 12a\)

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

**For example:**

Simplify: \(5× a×a+6×5×a\)

Here, in both the terms, \(5\) and \(a\) are common.

Thus, we can simplify the expression by taking the commons out i.e., \(5\) and \(a\).

\(5×a×a + 6× 5 ×a\)

\( = 5a (a+6)\)

A \(4b(2+3b)\)

B \(3b(b+2b)\)

C \(b(2+3b)\)

D \(b^2 (2+3b)\)

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

**For example:**

Simplify: \(6×b×b×b - 6×b×b\)

Here, \(6\) and two b's are common in both the terms.

Thus, we can simplify the expression by taking the commons out i.e., \(6\) and two b's.

\(6×b×b×b-6×b×b\)

\( = 6×b×b(b-1)\)

\( = 6b^2(b-1)\)

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

**For example:**

Simplify: \(\dfrac{6× d×d}{3d} + \dfrac{10×d×d×d}{5d×d}\)

In expressions involving division, similar variables in the numerator and the denominator get canceled by each other i.e.,

\(\dfrac{ \not{6}^2× \not{d}×d}{ \not{3}× \not{d}} + \dfrac{\not10^2×d× \not{d}× \not{d}}{\not5× \not{d}× \not{d}}\)

\( = 2d+2d\)

\( = 2d(1+1)\) [Taking the commons out i.e, 2d]

\(= 2d(2)\)

\(= 4d\)

A \(2e\)

B \(e (1+2e)\)

C \(e\)

D \(1+2e\)

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

**For example:**

Simplify: \(\dfrac{4×e×e}{2×e} - \dfrac{9×e×e×e}{3×e×e}\)

In expressions involving division, similar variables in the numerator and the denominator get canceled by each other i.e.,

\(\dfrac{ \not{4}^2 × \not{e}×e}{ \not{2}× \not{e}} - \dfrac{ \not{9}^3× \not{e}× \not{e}×e}{ \not{3}× \not{e}× \not{e}}\)

\( = 2e-3e\)

\(=e (2-3)\) [Taking \(e\) as common]

\(=e (-1)\)

\(= -e\)

A \(z-3\)

B \(2z-3\)

C \(2z\)

D \(2z(2z-3)\)

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

**For example: **

Simplify: \(\dfrac{3×z×5×z×z×z}{z×3×5×z}\)

In expressions involving division, similar variables in the numerator and the denominator get canceled by each other i.e.,

\(\dfrac{\not {3}×\not {z}×\not {5}×\not {z}×z×z}{\not {z}×\not {3}×\not {5}×\not {z}}\)

\(=z×z\)

\(=z^2\)