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Simplification Of Expressions (single Operation And Single Variable)

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: \(x+2x+3x\)

Here, we know that \(x, \;2x\) and \(3x\) are all like terms.

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

\(x+2x+3x\)

\( = x(1+2+3)\)

\( = x(6)\)

\( = 6x\)

Illustration Questions

Simplify the expression:  \(5y+6y+8y\)

A \(17 y\)

B \(18 y\)

C \(19 y\)

D \(20 y\)

×

Given expression: 

\(5y+6y+8y\)

We can simplify it by taking the common variable out i.e., \(y\).

Thus, \(5y + 6y + 8y \)

\(= y (5+6+8)\)

\( = y (19)\)

\(=19 y\)

Hence, option (C) is correct.

Simplify the expression:  \(5y+6y+8y\)

A

\(17 y\)

.

B

\(18 y\)

C

\(19 y\)

D

\(20 y\)

Option C is Correct

Simplification of Expressions involving  Subtraction

  • 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., subtraction.

For example: 

Simplify: \(20z-16z\)

Here, we know that \(20z\) and \(-16z\) are like terms.

We can simplify the expression by taking the common variable out i.e., z.

\(20z-16z = z(20-16)\)

\(= z (4)\)

\(= 4z\)

Illustration Questions

Simplify the expression: \(10a - 2a-3a\)

A \(10a\)

B \(4a\)

C \(6a\)

D \(5a\)

×

Given expression:

\(10a- 2a- 3a\)

We can simplify it by taking the common variable out i.e., \(a\).

Thus, \(10a-2 a-3a\)

\( = a(10-2-3)\)

\( = a (5)\)

\( = 5a\)

Hence, option (D) is correct.

Simplify the expression: \(10a - 2a-3a\)

A

\(10a\)

.

B

\(4a\)

C

\(6a\)

D

\(5a\)

Option D is Correct

Simplification of Expressions involving  Multiplication

  • 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., multiplication.

For example: 

Simplify: \(4×a×a×a×3 \)

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

\(4×a×a×a×3 \)

\(= 12×a×a×a\)

\( = 12 a^3\)

Illustration Questions

Simplify the expression: \(6×d×d×d×3×d×d\)

A \(18d^5\)

B \(6d^5\)

C \(3d^5\)

D \(\;d^5\)

×

Given expression:

\(6×d×d×d×3×d×d\)

We can simplify the expression by multiplying the numbers and counting the number of times the variable is multiplied by itself and writing it as the power of the variable.

Thus, \(6×d×d×d×3×d×d \)

\(= 18×d×d×d×d×d\)

\( = 18 d^5\)

Hence, option (A) is correct.

Simplify the expression: \(6×d×d×d×3×d×d\)

A

\(18d^5\)

.

B

\(6d^5\)

C

\(3d^5\)

D

\(\;d^5\)

Option A is Correct

Simplification of Expressions involving  Division

  • 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., division.

For example:

Simplify: \(\dfrac{4×a×a×a}{2×a×a}\) 

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

There are three a's in the numerator and two a's in the denominator.

Thus, the two a's in the numerator are canceled out by the two a's in the denominator.

\( = \dfrac{4×a×\not a×\not a}{2×\not a×\not a}\)

\( = \dfrac{4}{2}a\)

\( = 2a\)  \(\left[\because \dfrac{4}{2} = 2\right]\)

Illustration Questions

Simplify the expression: \(\dfrac{8×e×e×e×e×e}{2×e×e×e}\)

A \(8e^5\)

B \(4e^2\)

C \(2e^3\)

D \(4e^5\)

×

Given expression:

\(\dfrac{8×e×e×e×e×e}{2×e×e×e}\)

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

Thus, \(\dfrac{8×e×e×\not {e}×\not {e}×\not {e}}{2×\not {e}×\not {e}×\not {e}}\)

\( = \dfrac{8}{2} × e × e\)

\( = 4 × e× e\)

\(=4 e^2\)   [Writing in exponential  form]

Hence, option (B) is correct.

Simplify the expression: \(\dfrac{8×e×e×e×e×e}{2×e×e×e}\)

A

\(8e^5\)

.

B

\(4e^2\)

C

\(2e^3\)

D

\(4e^5\)

Option B is Correct

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