RD Sharma Class 7 Math 7th Chapter Algebraic Expressions Exercise 7.4 Solution

Exercise 7.4

 

Simplify, the algebraic expressions by removing grouping symbols.

 

1.  2x + (5x – 3y)

We get,

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

2. 3x – (y – 2x)

Solution:

Given 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

On simplifying, we get

= 5x – y

3. 5a – (3b – 2a + 4c)

Solution:

Given: 5a – (3b – 2a + 4c) = 5a – 3b + 2a – 4c

= 7a – 3b – 4c

4. -2(x2 – y2 + xy) – 3(x2 +y2 – xy)

Solution:

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. Therefore, we have

= -2x2 + 2y2 – 2xy – 3x2 – 3y2 + 3xy

= -2x2 – 3x2 + 2y2 – 3y2 – 2xy + 3xy

= -5x2 – y2 + xy

5. 3x + 2y – {x – (2y – 3)}

Solution:

Given 3x + 2y – {x- (2y – 3)

First, we have to remove the parentheses. Then, we have to remove the braces.

Then we get,

= 3x + 2y – {x-2y + 3}

= 3x + 2y – x+ 2y – 3

On simplifying, we get

= 2x + 4y – 3

6. 5a – {3a – (2 – a) + 4}

Solution:

We get,

5a – {3a – (2 – a) + 4}

First we remove to parentheses, than the braces and then the square brackets.

Therefore,

= 5a – {3a – 2 + a + 4}

= 5a – 3a + 2 – a – 4

= 5a – 4a – 2

= a – 2

7. a – [b – {a – (b – 1) + 3a}]

Solution:

First we remove to parentheses, than the braces 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

8. a – [2b – {3a – (2b – 3c)}]

Solution:

Given  a – [ 2b – { 32 – ( 2b -3c)}]

First we remove to parentheses, than the braces 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

9. -x + [5y – {2x – (3y – 5x)}]

Solution:

First we remove to parentheses, than the braces 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

10. Simplify, the algebraic expressions by removing grouping symbols.

 

2a – [4b – {4a – 3(2a – b)}]

Solution:

First we remove to parentheses, than the braces and then the square brackets.

Then we have,

= 2a – [ 4b – {4a – 3(2a – b)}]

= 2a – [4b – { 4a – 6a  – 6a + 3b})]

= 2a – [4b – { -2a + 3b}[

= 2a – [ 4b + 2a – 3b]

= 2a – [ b + 2a]

= 2a – b – 2a

= – b

11. Simplify, the algebraic expressions by removing grouping symbols.

 

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

Solution:

First we remove to parentheses, than the braces and then the square brackets.

Then 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

12. Simplify, the algebraic expressions by removing grouping symbols.

 

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

Solution:

First we remove to parentheses, than the braces and then the square brackets.

Then 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

13. Simplify, the algebraic expressions by removing grouping symbols.

 

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

Solution:

First we remove to parentheses, than the braces and then the square brackets.

Then 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

14. x2 – [3x + [2x – (x2 – 1)] + 2]

Solution:

First we remove to parentheses, than the braces and then the square brackets.

Then, 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

15. 20 – [5xy + 3[x2 – (xy – y) – (x – y)]]

Solution:

First we remove to parentheses, than the braces and then the square brackets.

Then, 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

= – 3×2 – 2xy – 6y + 3x + 20

16. 85 – [12x – 7(8x – 3) – 2{10x – 5(2 – 4x)}]

Solution:

First we remove to parentheses, than the braces and then the square brackets.

Then, 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

17. xy[yz – zx – {yx – (3y – xz) – (xy – zy)}]

Solution:

First we remove to parentheses, than the braces and then the square brackets.

Then, 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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