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**Simplify each of the following algebraic expressions by removing grouping symbols. − x + [5y − {2x − (3y − 5x)}]**

First we have to remove the small brackets, or parentheses, ( ), then the curly brackets, { }, and then the square brackets, [ ].

Therefore, we have

- x + [5y - {2x - (3y - 5x)}]

= - x + [5y - {2x - 3y + 5x}]

= - x + [5y - {7x - 3y}]

= - x + [5y - 7x + 3y]

= - x + [8y - 7x]

= - x + 8y - 7x

= - 8x + 8y

**Simplify each of the following algebraic expressions by removing grouping symbols. 2 a − [4b − {4a − 3(2a − b)}]**

First we have to remove the small brackets, or parentheses, ( ), then the curly brackets, { }, and then the square brackets, [ ].

Therefore, we have

2a - [4b - {4a - 3(2a - b)}]

= 2a - [4b - {4a - 6a + 3b}]

= 2a - [4b - {- 2a + 3b}]

= 2a - [4b + 2a - 3b]

= 2a - [b + 2a]

= 2a - b - 2a

= - b

**Simplify each of the following algebraic expressions by removing grouping symbols. − a − [a + {a + b − 2a − (a − 2b)} − b]**

First we have to remove the small brackets, or parentheses, ( ), then the curly brackets,{ }, and then the square brackets, [ ].

Therefore, we have

- a - [a + {a + b - 2a - (a - 2b)} - b]

= - a - [a + {a + b - 2a - a + 2b} - b]

= - a - [a + {- 2a + 3b} - b]

= - a - [a - 2a + 3b - b]

= - a - [- a + 2b]

= - a + a - 2b

= - 2b

**Simplify each of the following algebraic expressions by removing grouping symbols. 2 x − 3y − [3x − 2y − {x − z − (x − 2y)}]**

First we have to remove the small brackets, or parentheses, ( ), then the curly brackets, { }, and then the square brackets, [ ].

Therefore, we have

2x - 3y - [3x - 2y - {x - z - (x - 2y)}]

= 2x - 3y - [3x - 2y - {x - z - x + 2y}]

= 2x - 3y - [3x - 2y - {- z + 2y}]

= 2x - 3y - [3x - 2y + z - 2y]

= 2x - 3y - [3x - 4y + z]

= 2x - 3y - 3x + 4y - z

= - x + y - z

**Simplify each of the following algebraic expressions by removing grouping symbols. 5 + [ x − {2y − (6x + y − 4) + 2x} − {x − (y − 2)}]**

First we have to remove the small brackets, or parentheses, ( ), then the curly brackets, { }, and then the square brackets, [ ].

Therefore, we have

5 + [x - {2y - (6x + y - 4) + 2x} - {x - (y - 2)}]

= 5 + [x - {2y - 6x - y + 4 + 2x} - {x - y + 2}]

= 5 + [x - {y - 4x + 4} - {x - y + 2}]

= 5 + [x - y + 4x - 4 - x + y - 2]

= 5 + [4x - 6]

= 5 + 4x - 6

= 4x - 1

**Simplify each of the following algebraic expressions by removing grouping symbols. x^{2} − [3x + {2x − (x^{2} − 1) + 2}]**

First we have to remove the small brackets, or parentheses, ( ), then the curly brackets, { }, and then the square brackets, [ ].

Therefore, we have

x^{2} - [3x + {2x - (x^{2} - 1)} + 2]

= x^{2} - [3x + {2x - x^{2} + 1} + 2]

= x^{2} - [3x + 2x - x^{2} + 1+ 2]

= x^{2} - [5x - x^{2} + 3]

= x^{2} - 5x + x^{2} - 3

= 2x^{2} - 5x - 3

**Simplify each of the following algebraic expressions by removing grouping symbols. 20 − [5 xy + 3{x^{2} − (xy − y) − (x − y)}]**

First we have to remove the small brackets, or parentheses, ( ), then the curly brackets, { }, and then the square brackets, [ ].

Therefore, we have

20 - [5xy + 3{x^{2} - (xy - y) - (x - y)}]

= 20 - [5xy + 3{x^{2} - xy + y - x + y}]

= 20 - [5xy + 3{x^{2} - xy + 2y - x}]

= 20 - [5xy + 3x^{2} - 3xy + 6y - 3x]

= 20 - [2xy + 3x^{2} + 6y - 3x]

= 20 - 2xy - 3x^{2} - 6y + 3x

= - 3x^{2} - 2xy - 6y + 3x + 20

**Simplify each of the following algebraic expressions by removing grouping symbols. 85 − [12 x − 7(8x − 3) − 2 {10x − 5(2 − 4x)}]**

First we have to remove the small brackets, or parentheses, ( ), then the curly brackets, { }, and then the square brackets, [ ].

Therefore, we have

85 - [12x - 7(8x - 3) - 2{10x - 5(2 - 4x)}]

= 85 - [12x - 56x + 21 - 2{10x - 10 + 20x}]

= 85 - [12x - 56x + 21 - 2{30x - 10}]

= 85 - [12x - 56x + 21 - 60x + 20]

= 85 - [12x - 116x + 41]

= 85 - [- 104x + 41]

= 85 + 104x - 41

= 44 + 104x

**Simplify each of the following algebraic expressions by removing grouping symbols. xy [yz − zx − {yx − (3y − xz) − (xy − zy)}]**

First we have to remove the small brackets, or parentheses, ( ), then the curly brackets, { }, and then the square brackets, [ ].

Therefore, we have

xy - [yz - zx - {yx - (3y - xz) - (xy - zy)}]

= xy - [yz - zx - {yx - 3y + xz - xy + zy}]

= xy - [yz - zx - {- 3y + xz + zy}]

= xy - [yz - zx + 3y - xz - zy]

= xy - [- zx + 3y - xz]

= xy - [- 2zx + 3y]

= xy + 2xz - 3y

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- RD Sharma Solutions (Part -1) - Ex - 7.4, Algebraic Expressions, Class 7, Math
- RD Sharma Solutions - Ex - 7.3, Algebraic Expressions, Class 7, Math
- RD Sharma Solutions (Part - 3) - Ex - 7.2, Algebraic Expressions, Class 7, Math
- RD Sharma Solutions (Part - 2) - Ex - 7.2, Algebraic Expressions, Class 7, Math