RD Sharma Solutions for Class 8 Maths Chapter 6 - Algebraic Expressions and Identities Exercise 6.5

To excel in annual exams, students can access the free PDF of RD Sharma Solutions for Class 8 Maths Exercise 6.5 of Chapter 6 Algebraic Expressions and Identities which are provided here. BYJU’S experts have designed solutions to help students secure good marks in their exams by practising the RD Sharma Solutions thoroughly. The PDFs can be downloaded easily from the links given below. In Exercise 6.5 of Chapter 6, Algebraic Expressions and Identities, we will discuss problems based on the multiplication of two binomials.

RD Sharma Solutions for Class 8 Maths Exercise 6.5 Chapter 6 Algebraic Expressions and Identities

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Access Answers to RD Sharma Solutions for Class 8 Maths Exercise 6.5 Chapter 6 Algebraic Expressions and Identities

EXERCISE 6.5 PAGE NO: 6.30

Multiply:

1. (5x + 3) by (7x + 2)

Solution:

Now, let us simplify the given expression

(5x + 3) × (7x + 2)

5x (7x + 2) + 3 (7x + 2)

35x² + 10x + 21x + 6

35x² + 31x + 6

2. (2x + 8) by (x – 3)

Solution:

Now, let us simplify the given expression

(2x + 8) × (x – 3)

2x (x – 3) + 8 (x – 3)

2x² – 6x + 8x – 24

2x² + 2x – 24

3. (7x + y) by (x + 5y)

Solution:

Now, let us simplify the given expression

(7x + y) × (x + 5y)

7x (x + 5y) + y (x + 5y)

7x² + 35xy + xy + 5y²

7x² + 36xy + 5y²

4. (a – 1) by (0.1a² + 3)

Solution:

Now, let us simplify the given expression

(a – 1) × (0.1a² + 3)

a (0.1a² + 3) -1 (0.1a² + 3)

0.1a³ + 3a – 0.1a² – 3

0.1a³ – 0.1a² + 3a – 3

5. (3x² + y²) by (2x² + 3y²)

Solution:

Now, let us simplify the given expression

(3x² + y²) × (2x² + 3 y²)

3x² × (2x² + 3y²) + y² × (2x² + 3y²)

6x⁴ + 9x²y² + 2x²y² + 3y⁴

6x⁴ + 11x²y² + 3y⁴

6. (3/5x + 1/2y) by (5/6x + 4y)

Solution:

Now, let us simplify the given expression

(3/5x + 1/2y) × (5/6x + 4y)

3/5x × (5/6x + 4y) + 1/2y × (5/6x + 4y)

15/30x² + 12/5xy + 5/12xy + 4/2y²

1/2x² + 169/60xy + 2y²

7. (x⁶ – y⁶) by (x² + y²)

Solution:

Now, let us simplify the given expression

(x⁶ – y⁶) × (x² + y²)

x⁶ × (x² + y²) – y⁶ × (x² + y²)

x⁸ + x⁶y² – x²y⁶ – y⁸

8. (x² + y²) by (3a + 2b)

Solution:

Now, let us simplify the given expression

(x² + y²) × (3a + 2b)

x² × (3a + 2b) + y² × (3a + 2b)

3ax² + 3ay² + 2bx² + 2by²

9. (- 3d – 7f) by (5d + f)

Solution:

Now, let us simplify the given expression

(- 3d – 7f) × (5d + f)

-3d (5d + f) – 7f (5d + f)

– 15d² – 3df – 35df – 7f²

– 15d² – 38df – 7f²

10. (0.8a – o.5b) by (1.5a – 3b)

Solution:

Now, let us simplify the given expression

(0.8a – 0.5b) × (1.5a – 3b)

0.8a (1.5a – 3b) – 0.5b (1.5a – 3b)

1.2a² – 2.4ab – 0.75ab + 1.5b²

1.2a² – 3.15ab + 1.5b²

11. (2x²y² – 5xy²) by (x² – y²)

Solution:

Now, let us simplify the given expression

(2x²y² – 5xy²) × (x² – y²)

2x²y² (x² – y²) – 5xy² (x² – y²)

2x⁴y² – 5x³y² – 2x²y⁴ + 5xy⁴

12. (x/7 + x²/2) by (2/5 + 9x/4)

Solution:

Now, let us simplify the given expression

(x/7 + x²/2) × (2/5 + 9x/4)

x/7 (2/5 + 9x/4) + x²/2 (2/5 + 9x/4)

2x/35 + (9 x²)/28 + x²/5 + (9 x³)/8

9/8x³ + 73/140x² + 2/35x

13. (-a/7 + a²/9) by (b/2 – b²/3)

Solution:

Now, let us simplify the given expression

(-a/7 + a²/9) × (b/2 – b²/3)

-a/7 (b/2 – b²/3) + a²/9 (b/2 – b²/3)

-ab/14 + ab²/21 + a²b/18 – a²b²/27

14. (3x²y – 5xy²) by (1/5x² + 1/3y²)

Solution:

Now, let us simplify the given expression

(3x²y – 5xy²) × (1/5x² + 1/3y²)

3x²y (1/5x² + 1/3y²) – 5xy² (1/5x² + 1/3y²)

3/5x⁴y + 3/3x²y³ – x³y² + 5/3xy⁴

3/5x⁴y + x²y³ – x³y² + 5/3xy⁴

15. (2x² – 1) by (4x³ + 5x²)

Solution:

Now, let us simplify the given expression

(2x² – 1) × (4x³ + 5x²)

2x² (4x³ + 5x²) – 1 (4x³ + 5x²)

8x⁵ + 10x⁴ – 4x³ – 5x²

16. (2xy + 3y²) by (3y² – 2)

Solution:

Now, let us simplify the given expression

(2xy + 3y²) × (3y² – 2)

2xy (3y² – 2) + 3y² (3y² – 2)

6xy³ – 4xy + 9y⁴ – 6y²

Find the following products and verify the results for x = -1, y = -2:

17. (3x – 5y) (x + y)

Solution:

Now, let us simplify the given expression

(3x – 5y) × (x + y)

(3x – 5y) × (x + y)

x (3x – 5y) + y (3x – 5y)

3x² – 5xy + 3xy – 5y²

3x² – 2xy – 5y²

Let us substitute the given values x = – 1 and y = – 2, then

(3x – 5y) × (x + y)

(-3+10) × (-1-2)

7×-3

-21

3x² – 2xy – 5y²

3 (-1)² – 2 (-1) (-2) – 5 (-2)²

3 – 4 – 20

– 21

∴ the given expression is verified.

18. (x²y – 1) (3 – 2x²y)

Solution:

Now, let us simplify the given expression

(x²y – 1) × (3 – 2x²y)

x²y (3 – 2x²y) – 1 (3 – 2x²y)

3x²y – 2x⁴y² – 3 + 2x²y

5x²y – 2x⁴y² – 3

Let us substitute the given values x = – 1 and y = – 2, then

(x²y – 1) × (3 – 2x²y)

(-2 – 1) × (3 + 4)

-3 × 7

-21

5x²y – 2x⁴y² – 3

– 8 – 10 – 3

-21

∴ the given expression is verified.

19. (1/3x – y²/5) (1/3x + y²/5)

Solution:

Now, let us simplify the given expression

(1/3x – y²/5) × (1/3x + y²/5)

(1/3x) ² – (y²/5)²

(1/3x – y²/5) (1/3x + y²/5)

1/9x² – 1/25y⁴

Let us substitute the given values x = – 1 and y = – 2, then

(1/3x – y²/5) × (1/3x + y²/5)

(1/3(-1) – (-2)²/5) × (1/3(-1) + (-2)²/5)

(-17/15) × (7/15)

-119/225

1/9x² – 1/25y⁴

1/9 (-1)² – 1/25 (-2)⁴

1/9 -16/25

-119/225

∴ the given expression is verified.

Simplify:

20. x² (x + 2y) (x – 3y)

Solution:

Now, let us simplify the given expression

x² (x + 2y) (x – 3y)

x² (x² – 3xy + 2xy – 3y²)

x² (x² – xy – 6y²)

x⁴ – x³y – 6x²y²

21. (x² – 2y²) (x + 4y)x²y²

Solution:

Now, let us simplify the given expression

(x² – 2y²) (x + 4y)x²y²

(x³ + 4x²y – 2xy² – 8y³) × x²y²

x⁵y² + 4x⁴y³ – 2x³y⁴ – 8x²y⁵

22. a²b² (a + 2b) (3a + b)

Solution:

Now, let us simplify the given expression

a²b² (a + 2b) (3a + b)

a²b² (3a² + ab + 6ab + 2b²)

a²b² (3a² + 7ab + 2b²)

3a⁴b² + 7a³b³ + 2a²b⁴

23. x² (x – y) y² (x + 2y)

Solution:

Now, let us simplify the given expression

x² (x – y) y² (x + 2y)

x²y² (x² + 2xy – xy – 2y²)

x²y² (x² + xy – 2y²)

x⁴y² + x³y³ – 2x²y⁴

24. (x³ – 2x² + 5x – 7) (2x – 3)

Solution:

Now, let us simplify the given expression

(x³ – 2x² + 5x – 7) (2x – 3)

2x⁴ – 4x³ + 10x² – 14x – 3x³ + 6x² – 15x + 21

2x⁴ – 7x³ + 16x² – 29x + 21

25. (5x + 3) (x – 1) (3x – 2)

Solution:

Now let us simplify the given expression

(5x + 3) (x – 1) (3x – 2)

(5x² – 2x – 3) (3x – 2)

15x³ – 6x² – 9x – 10x² + 4x + 6

15x³ – 16x² – 5x + 6

26. (5 – x) (6 – 5x) (2 – x)

Solution:

Now, let us simplify the given expression

(5 – x) (6 – 5x) (2 – x)

(x² – 7x + 10) (6 – 5x)

-5x³ + 35x² – 50x + 6x² – 42x + 60

60 – 92x + 41x² – 5x³

27. (2x² + 3x – 5) (3x² – 5x + 4)

Solution:

Now, let us simplify the given expression

(2x² + 3x – 5) (3x² – 5x + 4)

6x⁴ + 9x³ – 15x² – 10x³ – 15x² + 25x + 8x² + 12x – 20

6x⁴ – x³ – 22x² + 37x – 20

28. (3x – 2) (2x – 3) + (5x – 3) (x + 1)

Solution:

Now, let us simplify the given expression

(3x – 2) (2x – 3) + (5x – 3) (x + 1)

6x² – 9x – 4x + 6 + 5x² + 5x – 3x – 3

11x² – 11x + 3

29. (5x – 3) (x + 2) – (2x + 5) (4x – 3)

Solution:

Now, let us simplify the given expression

(5x – 3) (x + 2) – (2x + 5) (4x – 3)

5x² + 10x – 3x – 6 – 8x² + 6x – 20x + 15

-3x² – 7x + 9

30. (3x + 2y) (4x + 3y) – (2x – y) (7x – 3y)

Solution:

Now, let us simplify the given expression

(3x + 2y) (4x + 3y) – (2x – y) (7x – 3y)

12x² + 9xy + 8xy

12x² + 9xy + 8xy + 6y² – 14x² + 6xy + 7xy – 3y²

-2x² + 3y² + 30xy

31. (x² – 3x + 2) (5x – 2) – (3x² + 4x – 5) (2x – 1)

Solution:

Now, let us simplify the given expression

(x² – 3x + 2) (5x – 2) – (3x² + 4x – 5) (2x – 1)

5x³ – 15x² + 10x – 2x² + 6x – 4 – (6x³ + 8x² – 10x – 3x² – 4x + 5)

5x³ – 6x³ – 15x² – 2x² – 5x² + 16x + 14x – 4 – 5

– x³ – 22x² + 30x – 9

32. (x³ – 2x² + 3x – 4) (x – 1) – (2x – 3) (x² – x + 1)

Solution:

Now, let us simplify the given expression

(x³ – 2x² + 3x – 4) (x – 1) – (2x – 3) (x² – x + 1)

x⁴ – 2x³ + 3x² – 4x – x³ + 2x² – 3x + 4 – (2x³ – 2x² + 2x – 3x² + 3x – 3)

x⁴ – 3x³ + 5x² – 7x + 4 – 2x³ + 5x² – 5x + 3

x⁴ – 5x³ + 10x² – 12x + 7