Informative line

Simplification Of Expressions (single Operation And Multiple Variables)

• Simplification means making things easier.
• We can simplify the expressions having various operations.
• Here, we will learn to simplify the expressions having only one operation i.e., addition.

For example:

Simplify: $$3x+5y+2y+3x$$

First, arrange the like terms together.

$$3x+3x+5y+2y$$

Now, take the common variables out

$$3x(1+1)+y (5+2)$$

$$= 3x(2)+y(7)$$

$$=6x+7y$$

Simplify the expression: $$2x+5y+3x+2y$$

A $$5x+7y$$

B $$6x+7y$$

C $$7x+5y$$

D $$12xy$$

×

Given expression:

$$2x+5y+3x+2y$$

First, arrange the like terms together.

Next, take the common variables out.

$$2x+5y+3x+2y$$

$$= 2x+3x+5y+2y$$

$$=x(2+3)+y (5+2)$$

$$=x (5)+y (7)$$

$$= 5x+7y$$

Hence, option (A) is correct.

Simplify the expression: $$2x+5y+3x+2y$$

A

$$5x+7y$$

.

B

$$6x+7y$$

C

$$7x+5y$$

D

$$12xy$$

Option A is Correct

Simplification of Expressions involving Subtraction

• Here, we will learn to simplify the expressions involving subtraction.

For example:

Simplify: $$5y-3x-2x-y$$

First, arrange the like terms together.

$$5y-y-3x-2x$$

Now, take the common variables out.

$$y(5-1)+x(-3-2)$$

$$= y (4)+x(-5)$$

$$=4y-5x$$

Simplify the expression: $$7a-2b-c-3b-2c$$

A $$7a-b-c$$

B $$7a-5b-3c$$

C $$a-5b-3c$$

D $$7a-2b-c$$

×

Given expression:

$$7a-2b-c-3b-2c$$

First, arrange the like terms together and then take the common variables out.

$$7a-2b-c-3b-2c$$

$$= 7a-2b-3b-c-2c$$

$$=7a+b(-2-3)+c(-1-2)$$

$$=7a+b(-5)+c(-3)$$

$$= 7a-5b-3c$$

Hence, option (B) is correct.

Simplify the expression: $$7a-2b-c-3b-2c$$

A

$$7a-b-c$$

.

B

$$7a-5b-3c$$

C

$$a-5b-3c$$

D

$$7a-2b-c$$

Option B is Correct

Simplification of Expressions involving  Multiplication

• Here, we will learn to simplify the expressions involving multiplication.

For example:

Simplify: $$4×a×a×b×2×c×b$$

Here, we will multiply the numbers and count the number of times each variable is multiplied by itself and write it as the power of that variable i.e.

$$4×a×a×b×2×c×b$$

$$= 4 ×2×a×a×b×b×c$$

$$= 8a^2b^2c$$

Simplify the expression: $$5×z×y×z×y×z×y$$

A $$5zy$$

B $$z^3y^3$$

C $$5z^2y^2$$

D $$5z^3y^3$$

×

Given expression:

$$5×z×y×z×y×z×y$$

Multiply the numbers and count the number of times each variable is multiplied by itself and write it as the power of that variable i.e.

$$5×z×y×z×y×z×y$$

$$=5 ×z×z×z×y×y×y$$

$$= 5z^3y^3$$

Hence, option (D) is correct.

Simplify the expression: $$5×z×y×z×y×z×y$$

A

$$5zy$$

.

B

$$z^3y^3$$

C

$$5z^2y^2$$

D

$$5z^3y^3$$

Option D is Correct

Simplification of Expressions involving Division

• Here, we will learn to simplify the expressions involving division.

For example:

Simplify: $$\dfrac{16×a×b×a×b×c}{2×c×a×b×8}$$

In such type of expressions, we can cancel out the same variables appearing in both numerator and denominator i.e.,

$$\dfrac{16×a× \not{a}× \not{b}×b× \not{c}}{2×8× \not{a}× \not{b}× \not{c}}$$

$$=ab$$

Simplify the expression: $$\dfrac{10×m×m×m×n×n×p×p}{5×m×m×p}$$

A $$10mn^2p^2$$

B $$2mn^2p$$

C $$m^3np$$

D $$mn^2$$

×

Given expression:

$$\dfrac{10×m×m×m×n×n×p×p}{5×m×m×p}$$

In expressions involving division, we can cancel out the same variables appearing in both numerator and denominator i.e.,

$$\dfrac{\not10^2×m× \not{m}× \not{m}×n×n×p× \not{p}}{\not5× \not{m}× \not{m}× \not{p}}$$

$$= 2mn^2p$$

Hence, option (B) is correct.

Simplify the expression: $$\dfrac{10×m×m×m×n×n×p×p}{5×m×m×p}$$

A

$$10mn^2p^2$$

.

B

$$2mn^2p$$

C

$$m^3np$$

D

$$mn^2$$

Option B is Correct