Informative line

# Simplification of Expressions involving Addition and Subtraction

• 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, $$5a+6a-7a+8a$$

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

$$= a (19-7)$$

$$= a (12)$$

$$= 12a$$

#### Simplify the expression: $$7z+2z-3z-2z$$

A $$2z$$

B $$7z$$

C $$4z$$

D $$3z$$

×

Given expression:

$$7z + 2z-3z-2z$$

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

Thus, $$7z+2z-3z-2z$$

$$=z(7+2-3-2)$$

$$= z (4)$$

$$= 4z$$

Hence, option (C) is correct.

### Simplify the expression: $$7z+2z-3z-2z$$

A

$$2z$$

.

B

$$7z$$

C

$$4z$$

D

$$3z$$

Option C is Correct

# Simplification of Expressions involving Addition and Multiplication

• 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 $$a$$.

$$5×a×a + 6× 5 ×a$$

$$= 5a (a+6)$$

#### Simplify the expression: $$2 × b×b+3×b×b×b$$

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

B $$3b(b+2b)$$

C $$b(2+3b)$$

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

×

Given expression:

$$2× b×b + 3 × b× b×b$$

Here, in both the terms, two b's are common.

Thus, we can simplify the expression by taking the commons out i.e., $$b×b$$.

Thus, $$2×b×b + 3× b×b×b$$

$$= b×b (2+3×b)$$

$$= b^2 (2+3b)$$

Hence, option (D) is correct.

### Simplify the expression: $$2 × b×b+3×b×b×b$$

A

$$4b(2+3b)$$

.

B

$$3b(b+2b)$$

C

$$b(2+3b)$$

D

$$b^2 (2+3b)$$

Option D is Correct

# Simplification of Expressions involving Subtraction and Multiplication

• 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.

$$6×b×b×b-6×b×b$$

$$= 6×b×b(b-1)$$

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

#### Simplify the expression: $$3×c×c-6×c$$

A $$3c(c-2)$$

B $$c-2$$

C $$3c$$

D $$6c$$

×

Given expression:

$$3×c×c - 6×c$$

Here, $$3$$ and $$c$$ are common in both the terms.

Thus, we can simplify the expression by taking the commons out i.e., $$3$$ and $$c$$.

Thus, $$3×c×c-6×c$$

$$= 3×c(c-2)$$

$$= 3c (c-2)$$

Hence, option (A) is correct.

### Simplify the expression: $$3×c×c-6×c$$

A

$$3c(c-2)$$

.

B

$$c-2$$

C

$$3c$$

D

$$6c$$

Option A is Correct

# Simplification of Expressions involving Addition and Division

• 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]

$$= 2d(2)$$

$$= 4d$$

#### Simplify the expression: $$\dfrac{2×e×e}{2×e} + \dfrac{6×e×e×e}{3×e}$$

A $$2e$$

B $$e (1+2e)$$

C $$e$$

D $$1+2e$$

×

Given expression:

$$\dfrac{2×e×e}{2×e} + \dfrac{6×e×e×e}{3×e}$$

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

$$\dfrac{ \not{2}× \not{e}×e}{ \not{2}× \not{e}} + \dfrac{ \not{6}^2× \not{e}×e×e}{ \not{3}× \not{e}}$$

$$=e + 2e×e$$

$$= e (1+2e)$$   [$$e$$ is common in both the terms]

Hence, option (B) is correct.

### Simplify the expression: $$\dfrac{2×e×e}{2×e} + \dfrac{6×e×e×e}{3×e}$$

A

$$2e$$

.

B

$$e (1+2e)$$

C

$$e$$

D

$$1+2e$$

Option B is Correct

# Simplification of Expressions involving Subtraction and Division

• 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]

$$=e (-1)$$

$$= -e$$

#### Simplify the expression: $$\dfrac{12×z×z×z}{3×z} - \dfrac{6×z×z}{z}$$

A $$z-3$$

B $$2z-3$$

C $$2z$$

D $$2z(2z-3)$$

×

Given expression:

$$\dfrac{12×z×z×z}{3×z} - \dfrac{6×z×z}{z}$$

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

$$\dfrac{\not12^4× \not{z}×z×z}{\not3× \not{z}} - \dfrac{6× \not{z}×z}{ \not{z}}$$

$$= 4 × z×z- 6×z$$

$$= 2×z (2×z-3)$$  [Taking $$2z$$ as common]

$$= 2z (2z-3)$$

Hence, option (D) is correct.

### Simplify the expression: $$\dfrac{12×z×z×z}{3×z} - \dfrac{6×z×z}{z}$$

A

$$z-3$$

.

B

$$2z-3$$

C

$$2z$$

D

$$2z(2z-3)$$

Option D is Correct

# Multiplication and Division

• 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.,

$$\dfrac{\not {3}×\not {z}×\not {5}×\not {z}×z×z}{\not {z}×\not {3}×\not {5}×\not {z}}$$

$$=z×z$$

$$=z^2$$

#### Simplify the expression: $$\dfrac{10×a×a×a×5}{a×5×a}$$

A $$2a$$

B $$5a$$

C $$10a$$

D $$12a$$

×

Given expression:

$$\dfrac{10×a×a×a×5}{a×5×a}$$

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

$$\dfrac{10×a×\not {a}×\not {a}×\not {5}}{\not {a}×\not {5}×\not {a}}$$

$$= 10a$$

Hence, option (C) is correct.

### Simplify the expression: $$\dfrac{10×a×a×a×5}{a×5×a}$$

A

$$2a$$

.

B

$$5a$$

C

$$10a$$

D

$$12a$$

Option C is Correct