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Simplification Of Expressions (single Operation And Multiple Variables)

Simplification of Expressions involving Addition

  • 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 

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

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

\(=6x+7y\)

Illustration Questions

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.

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

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

\(=4y-5x\)

Illustration Questions

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.

\(4×a×a×b×2×c×b\)

\(= 4 ×2×a×a×b×b×c\)

\(= 8a^2b^2c\)

Illustration Questions

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.,

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

\(=ab\)

Illustration Questions

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

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