RD Sharma Solutions (Part -1) - Ex - 7.4, Algebraic Expressions, Class 7, Math | RD Sharma Solutions for Class 7 Mathematics PDF Download

Question 1:

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

Answer 1:

We have 
   2x + (5x − 3y)
Since the '+' sign precedes the parentheses, we have to retain the sign of each term in the parentheses when we remove them.
= 2x + 5x - 3y
= 7x - 3y

Question 2:

Simplify each of the following algebraic expressions by removing grouping symbols.
 3x − (y − 2x)

Answer 2:

We have
3x − (y − 2x)
Since the '-' sign precedes the parentheses, we have to change the sign of each term in the parentheses when we remove them. Therefore, we have
3x − y + 2x
= 5x - y

Question 3:

Simplify each of the following algebraic expressions by removing grouping symbols.
 5a − (3b − 2a + 4c)

Answer 3:

We have
5a − (3b − 2a + 4c)
Since the '-' sign precedes the parentheses, we have to change the sign of each term in the parentheses when we remove them.
= 5a - 3b + 2a - 4c
= 7a - 3b - 4c

Question 4:

Simplify each of the following algebraic expressions by removing grouping symbols.
 −2 (x² − y² + xy) − 3(x² + y² − xy)

Answer 4:

We have
− 2(x² − y² + xy) − 3(x² + y² − xy)
Since the '-' sign precedes the parentheses, we have to change the sign of each term in the parentheses when we remove them.
= - 2x² + 2y² - 2xy - 3x² - 3y² + 3xy
= - 2x² - 3x² + 2y²- 3y² - 2xy + 3xy
= - 5x² - y² + xy

Question 5:

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

Answer 5:

We have
3x + 2y − {x − (2y − 3)}
First, we have to remove the small brackets (or parentheses): ( ). Then, we have to remove the curly brackets (or braces): { }.
Therefore,
= 3x + 2y − {x − 2y + 3}
= 3x + 2y − x + 2y - 3
= 2x + 4y - 3

Question 6:

Simplify each of the following algebraic expressions by removing grouping symbols.
 5a − {3a − (2 − a) + 4}

Answer 6:

We have
5a − {3a − (2 − a) + 4}
First, we have to remove the small brackets (or parentheses): ( ). Then, we have to remove the curly brackets (or braces): { }.
Therefore,
= 5a − {3a − 2 + a + 4}
= 5a − 3a + 2 - a - 4
= 5a - 4a - 2
= a - 2

Question 7:

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

Answer 7:

First we have to remove the parentheses, or small brackets, ( ), then the curly brackets, { }, and then the square brackets [ ].
Therefore, we have
a - [b - {a - (b - 1) + 3a}]
= a - [b - {a - b + 1 + 3a}]
= a - [b - {4a - b + 1}]
= a - [b - 4a + b - 1]
= a - [2b - 4a - 1]
= a - 2b + 4a + 1
= 5a - 2b + 1

Question 8:

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

Answer 8:

First we have to remove the small brackets, or parentheses, ( ), then the curly brackets, { }, and then the square brackets, [ ].
Therefore, we have
a - [2b - {3a - (2b - 3c)}]
= a - [2b - {3a - 2b + 3c}]
= a - [2b - 3a + 2b - 3c]
= a - [4b - 3a - 3c]
= a - 4b + 3a + 3c
= 4a - 4b + 3c