RS Aggarwal Class 6 Maths Solutions Chapter 8- Algebraic Expression Exercise 8D

RS Aggarwal 2021-2022 for Class 6 Maths Solutions Chapter 8- Algebraic Expression

RS Aggarwal Class 6 Math Solution Chapter 8- Algebraic Expression Exercise 8D is available here. RS Aggarwal Class 6 Math Solutions are solved by expert teachers in step by step, which help the students to understand easily.  RS Aggarwal textbooks are responsible for a strong foundation in Maths. These textbook solutions help students in exams as well as their daily homework routine. The solutions included are easy to understand, and each step in the solution is described to match the students’ understanding.

 Rs Aggarwal Class 6 Math Solution Chapter 8- Algebraic Expression 

Exercise 8D

1.  `a` – `(b  – 2a)`

Solution: 

    `a` – `(b  – 2a)`

    = `a – b + 2a`

    = `a + 2a  – b`

    = `3a  – b`

2. `4x  – (3y  – x + 2z)`

Solution: 

    `4x  – (3y  – x + 2z)`

    = `4x – 3y + x – 2z`

    = `4x + x  – 3y  – 2z`

    = `5x  – 3y  – 2z`

3. `(a^2 + b^2 + 2ab) – (a^2 + b^2 – 2ab)`

Solution: 

    `(a^2 + b^2 + 2ab) – (a^2 + b^2 – 2ab)`

    = `a^2 + b^2 + 2ab – a^2 – b^2 + 2ab`

    = `cancel (a^2) – cancel (a^2) + cancel (b^2) – cancel (b^2) + 2ab + 2ab`

    = `4 ab` 

4. `– 3 (a + b) + 4 (2a  – 3b)  – (2a  – b)`

Solution: 

     `– 3 (a + b) + 4 (2a  – 3b)  – (2a  – b)`

    = `– 3a  – 3b + 8a  – 12b  – 2a + b`

    = `– 3a + 8a   – 2a  – 3b   – 12b + b`

    = `– 5a + 8a  – 15b + b`

    = `3a  – 14 b`

5. `– 4x^2 + {(2x^2 – 3)  – (4  – 3x^2)}`

Solution: 

    `– 4x^2 + {(2x^2 – 3)  – (4  – 3x^2)}`

    = `– 4x^2 + {2x^2 – 3  – 4 + 3x^2}`

    [removing small bracket]

    = `– 4x^2 + {5x^2 – 7}`

    = `– 4x^2 + 5x^2 – 7`

    (removing curly bracket)

    = `x^2 – 7` 

6. `– 2 (x^2 – y^2 + xy) – 3 (x^2 + y^2 – xy)`

Solution: 

    `– 2 (x^2 – y^2 + xy) – 3 (x^2 + y^2 – xy)`

    = `– 2x^2 + 2y^2 – 2xy – 3x^2 – 3y^2 + 3xy`

    = `– 2x^2 – 3x^2 + 2y^2 – 3y^2 – 2xy + 3xy`

    = `– 5x^2 – y^2 + xy` 

7. `a – [2b – {3a – (2b – 3c)}]`

Solution: 

     `a – [2b – {3a – (2b – 3c)}]`

    = `a – [2b  – {3a  – 2b + 3c}]`

    [removing small bracket ()]

    = `a  – [2b  – 3a + 2b  – 3c]`

    (removing curly bracket {})

    = `a  – [4b  – 3a  – 3c]`

    = `a  – 4b + 3a + 3c`

    (removing big bracket [ ])

    = `4a  – 4b + 3c`

8. `– x + [5y  – {x  – (5y  – 2x)}]`

Solution: 

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

    = `– x + [5y  – {x  – 5y + 2x}]`

    = `– x + [5y  – {3x  – 5y}]`

    = `– x + [5y  – 3x + 5y]`

    = `– x + [ 10y  – 3x]`

    = `– x + 10y  – 3x`

    = `– x  – 3x + 10y`

    = `– 4x + 10y`

9. `86  – [15x  – 7 (6x  – 9)  – 2 {10x  – 5(2  – 3x)}]`

Solution: 

     `86  – [15x  – 7 (6x  – 9)  – 2 {10x  – 5(2  – 3x)}]`

    = `86  – [15x  – 42x + 63  – 2 {10x  – 10 + 15x}]`

    = `86  – [ 15x  – 42x + 63  – 2 {25x  – 10}]`

    = `86  – [15x  – 42x + 63  – 50x + 20]`

    = `86  – 15x + 42x  – 63 + 50x  – 20`

    = `86  – 63  – 20   – 15x + 42x + 50x`

    = `86  – 83  – 15x + 92x`

    = `3 + 77x`

10. `12x – [3x^3 + 5x^2 – {7x^2 – (4 – 3x – x^3) + 6x^3} – 3x]`

Solution: 

     `12x – [3x^3 + 5x^2 – {7x^2 – (4 – 3x – x^3) + 6x^3} – 3x]`

    = `12x – [3x^3 + 5x^2 – {7x^2 – 4 + 3x + x^3 + 6x^3} – 3x]`

    = `12x – [3x^3 + 5x^2 – {7x^2 – 4 + 3x + 7x^3} – 3x]`

    = `12x – [3x^3 + 5x^2 – 7x^2 + 4 – 3x – 7x^3 – 3x]`

    = `12x – [3x^3 – 7x^3 + 5x^2 – 7x^2 + 4 – 3x – 3x]`

    = `12x – [ – 4x^3 + 2x^2 + 4 – 6x]`

    = `12x + 4x^3 + 2x^2 – 4 + 6x`

    = `12x + 6x + 4x^3 + 2x^2 – 4`

    = `18x + 4x^3 + 2x^2 – 4`

    = `4x^3 + 2x^2 + 18x – 4`

11. `5a – [a^2 – {2a (1 – a + 4a^2) – 3a (a^2 – 5a – 3)}] – 8a`

Solution: 

    = `5a – [a^2 – {2a – 2a^2 + 8a^3 – 3a^3 + 15a^2 + 9a}] – 8a`

    = `5a – [a^2 – {2a + 9a – 2a^2 + 15a^2 + 8a^3 – 3a^3}] – 8a`

    = `5a – [a^2 – {11a + 13a^2 + 5a^3}] – 8a`

    = `5a – [a^2 – 11a – 13a^2 – 5a^3] – 8a`

    = `5a – a^2 + 11a + 13a^2 + 5a^3 – 8a`

    = `5a + 11a – 8a – a^2 + 13a^2 + 5a^3`

    = `8a + 12a^2 + 5a^3`

    = `5a^3 + 12a^2 + 8a`.

12. `3 – [x – {2y – (5x + y – 3) + 2x^2} – (x^2 – 3y)]`

Solution: 

    `3 – [x – {2y – (5x + y – 3) + 2x^2} – (x^2 – 3y)]`

    = `3 – [x – {2y – 5x – y + 3 + 2x^2} – x^2 + 3y]`

    = `3 – [x – {y – 5x + 3 + 2x^2} – x^2 + 3y]`

    = `3 – [x – y + 5x – 3 – 2x^2 – x^2 + 3y]`

    = `3 – [6x + 2y – 3 – 3x^2]`

    = `3 – 6x – 2y + 3 + 3x^2`

    = `6 – 6x – 2y + 3x^2`

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

Solution: 

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

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

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

    = `xv – [yz – zx – {- 3y + xz + zy}]`

    = `xy – [yz – zx + 3y – xz – zy]`

    = `xy – [ – 2xz + 3y]`

    = `xy + 2xz – 3y`

14. `2a – 3b – [3a – 2b – {a – c – (a – 2b)}]`

Solution: 

    `2a – 3b – [3a – 2b – {a – c – (a – 2b)}]`

    = `2a – 3b – [3a – 2b – {cancel (a) – c – cancel (a) + 2b}]`

    = `2a – 3b – [3a – 2b – { – c + 2b}]`

    = `2a – 3b – [3a – 2b + c – 2b]`

    = `2a – 3b – 3a + 2b – c + 2b`

    = `2a – 3a – 3b + 2b + 2b – c`

    = `– a + b – c`

15. `– a – [a + {a + b – 2a – (a – 2b)} – b]`

Solution: 

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

    = `– a – [a + {cancel (a) + b – 2a – cancel (a) + 2b} – b]`

    = `– a – [a + { – 2a + 3b} – b]`

    = `– a – [a – 2a + 3b – b]`

    = `– a – a + 2a – 3b + b`

    = `–cancel (2a) + cancel (2a) – 2b`

    = `– 2 b`

16. `2a – [4b – {4a – (3b – bar (2a+2b))}]`

Solution: 

    `2a – [4b – {4a – (3b – bar (2a+2b))}]`

    = `2a – [4b – {4a – (3b – 2a – 2b)}]`

    = `2a – [4b – {4a – (b – 2a)}]`

    = `2a – [4b – {4a – b + 2a}]`

    = `2a – [4b – {6a – b}]`

    = `2a – [4b – 6a + b]`

    = `2a – [5b – 6a]`

    = `2a – 5b + 6a`

    = `8a – 5b`.

17. `5x – [4y – {7x – (3z – 2y) + 4z – 3(x + 3y – 2z)}]`

Solution: 

    `5x – [4y – {7x – (3z – 2y) + 4z – 3(x + 3y – 2z)}]`

    = `5x – [4y – {7x – 3z + 2y + 4z – 3x – 9y + 6z}]`

    = `5x – [4y – {4x + 7z – 7y}]`

    = `5x – [4y – 4x – 7z + 7y]`

    = `5x – [11y – 4x – 7z]`

    = `5x – 11y + 4x + 7z`

    = `9x – 11y + 7z`