RD Sharma Solutions (Part -2) - Ex - 7.4, Algebraic Expressions, Class 7, Math | RD Sharma Solutions for Class 7 Mathematics PDF Download

Question 9:

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

Answer 9:

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

Question 10:

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

Answer 10:

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

Question 11:

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

Answer 11:

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

Question 12:

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

Answer 12:

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

Question 13:

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

Answer 13:

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

Question 14:

Simplify each of the following algebraic expressions by removing grouping symbols.
x² − [3x + {2x − (x² − 1) + 2}]

Answer 14:

First we have to remove the small brackets, or parentheses, ( ), then the curly brackets, { }, and then the square brackets, [ ].
Therefore, we have
x² - [3x + {2x - (x² - 1)} + 2]
= x² - [3x + {2x - x² + 1} + 2]
= x² - [3x + 2x - x² + 1+ 2]
= x² - [5x - x² + 3]
= x² - 5x + x² - 3
= 2x² - 5x - 3

Question 15:

Simplify each of the following algebraic expressions by removing grouping symbols.
 20 − [5xy + 3{x² − (xy − y) − (x − y)}]

Answer 15:

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{x² - (xy - y) - (x - y)}]
= 20 - [5xy + 3{x² - xy + y - x + y}]
= 20 - [5xy + 3{x² - xy + 2y - x}]
= 20 - [5xy + 3x² - 3xy + 6y - 3x]
= 20 - [2xy + 3x² + 6y - 3x]
= 20 - 2xy - 3x² - 6y + 3x
= - 3x² - 2xy - 6y + 3x + 20

Question 16:

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

Answer 16:

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

Question 17:

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

Answer 17:

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