Class 8 RD Sharma Solutions - Chapter 6 Algebraic Expressions And Identities - Exercise 6.5 | Set 1

Multiply the following:

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

Solution:

To find the product  of (5x + 3) (7x+2)    [use distributive property] 

⇒ (5x + 3) (7x + 2)

⇒ 5x(7x+2) + 3(7x+2)

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

⇒ 35x² + 10x + 21x + 6

⇒ 35x² + 31x + 6

The required answer is 35x² + 31x + 6

Question 2. (2x + 8) by (x - 3)

Solution:

To find the product of (2x + 8) (x - 3)    [use distributive property] 

⇒ (2x+8) (x - 3)

⇒ 2x (x - 3) + 8 (x - 3)

⇒ (2x × x - 2x × 3) + (8 × x - 8 × 3)

⇒ (2x² - 6x) + (8x - 24)

⇒ 2x² + 2x -24

The required answer is 2x² + 2x -24

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

Solution:

To find the product of  (7x + y) (x + 5y)     [ use distributive property ] 

⇒ 7x (x + 5y) + y (x + 5y)

⇒ (7x × x + 7x × 5y) + (y × x + y × 5y)

⇒ (7x² + 35xy) + (xy + 5y²)

⇒ 7x² + 36xy + 5y²

The required answer is 7x² + 36xy + 5y²

Question 4. (a - 1) by (0.1a² + 3)

Solution:

To find the product of (a - 1) (0.1a² + 3)    [use distributive property] 

⇒ a (0.1a² + 3) -1(0.1a² +3)

⇒ 0.1a³ +3a - 0.1a² - 3

⇒ 0.1a³ - 0.1a² +3a - 3

The required answer is 0.1a³ - 0.1a² + 3a - 3

Question 5. (3x² + y²) by (2x² + 3y²)

Solution:

To find the product of (3x² + y²) (2x² + 3y²)    [use distributive property] 

⇒ 3x²(2x² + 3y²) + y²(2x²+3y²)

⇒ 6x⁴ + 9x²y² + 2x²y² + 3y⁴

⇒ 6x⁴ + 11x²y² + 3y⁴

The required answer is 6x⁴ + 11x²y² + 3y⁴

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

Solution:

To find the product of (3/5x +1/2y) (5/6x + 4y)   [ use distributive property ] 

⇒ 3/5x(5/6x + 4y) + 1/2y(5/6x + 4y)

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

⇒ 1/2x² + 12/5xy + 5/12xy + 2y²

⇒ 1/2x² + 169/60 xy + 2y² 

The required answer is 1/2x² + 169/60xy + 2y² 

Question 7. (x⁶ - y⁶) by (x² + y²)

Solution:

To find the product of (x⁶ - y⁶) (x² + y²)   [ use distributive property ] 

⇒ x⁶ (x² + y²) - y⁶(x² + y²)

⇒ x⁸ + x⁶y² - y⁶x² - y⁸

The required answer is x⁸ + x⁶y² - y⁶x² - y⁸

Question 8. (x² + y²) by (3a + 2b)

Solution:

To find the product of (x²+y²) (3a + 2b)    [use distributive property] 

⇒ x²(3a + 2b) + y²(3a + 2b)

⇒ 3ax² + 2bx² + 3ay² + 2by²

The required answer is 3ax² + 2bx² + 3ay² + 2by²            

Question 9. [-3d + (-7f)] by (5d + f)

Solution:

To find the product of [-3d + (-7f)]  (5d + f)   [ use distributive property ] 

⇒ (-3d) (5d + f) + (-7f) (5d + f)

⇒ (-15d²) + (-3df) + (-35fd) + (-7f²)

⇒ -15d² -3df -35df -7f²

⇒ -15d² - 38df - 7f²

The required answer is -15d² - 38df -7f²

Question 10. (0.8a - 0.5b) by (1.5a - 3b)

Solution:

To find the product of (0.8a - 0.5b) (1.5a - 3b)   [use distributive property] 

⇒ 0.8a( 1.5a -3b) - 0.5b(1.5a - 3b)

⇒  1.2a² - 2.4ab - 0.75ab + 1.5b²

⇒ 1.2a2 + 1.5b2 - 3.15ab  

The required answer is 1.2a² + 1.5b² - 3.15ab 

Question 11. (2x²y² - 5xy²) by (x² - y²) 

Solution:

To find the product of (2x²y² - 5xy²) (x² - y²)    [use distributive property] 

⇒ 2x²y² (x² - y²) -5xy² (x² - y²)

⇒ 2x⁴y² - 2x²y⁴ -5x³y² + 5xy⁴

The required answer is 2x⁴y² - 2x²y⁴ - 5x³y² + 5xy⁴  

Question 12. (x/7 + x²/2) by (2/5 + 9x/4) 

Solution:

To find the product of (x/7 + x²/2) (2/5 + 9x/4)     [use distributive property] 

⇒ x/7(2/5 + 9x/4) + x²/2(2/5 + 9x/4)

⇒ 2x/35 + 9x²/28 + x²/5 + 9x³/8

⇒ 2x/35 + (9/28 + 1/5)x² + 9x³/8

⇒ 2x/35 + (45+28/140) x² + 9x³/8

⇒ 2x/35 + 73/140x² + 9x³/8

The required answer is 2x/35 + 73/140x² + 9x³/8

Question 13. (-a/7 + a²/9) by (b/2 - b²/3) 

Solution:

To find the product of (-a/7 + a²/9) by (b/2 - b²/3)    [ use distributive property ] 

⇒ (-a/7) (b/2 -b²/3) + a²/9 (b/2 - b²/3)

⇒ -ab/14 + ab²/21 + a²b/18 - a²b²/27

The required answer is -ab/14 + ab²/21 + a²b/18 - a²b²/27

Question 14. (3x²y - 5xy² ) by (1/5x² + 1/3y²) 

Solution:

To find the product of (3x²y -5xy²) (1/5x² + 1/3y²)     [ use distributive property ] 

⇒ 3x²y(1/5x² + 1/3y²) -5xy²(1/5x² + 1/3y²)

⇒ 3/5x⁴y + x²y³ - x³y² -5/3xy⁴

The required answer is 3/5x⁴y + x²y³ - x³y² -5/3xy⁴

Question 15. (2x² - 1) by (4x³ + 5x² )

Solution:

To find the product of (2x² - 1) (4x³ + 5x²)     [use distributive property] 

⇒ 2x² (4x³ + 5x² ) -1(4x³ + 5x²)

⇒ 8x⁵ + 10x⁴ - 4x³ - 5x² 

The required answer is 8x⁵ + 10x⁴ - 4x³ - 5x²

Question 16. (2xy + 3y²) by (3y² - 2)

Solution:

To find the product of (2xy + 3y²) (3y² - 2)     [ use distributive property ] 

⇒ 2xy (3y² - 2) + 3y² (3y² - 2) 

⇒ 6xy³ - 4xy + 9y⁴ - 6y²

The required answer is 6xy³ - 4xy + 9y⁴ - 6y² 

Chapter 6 Algebraic Expressions And Identities - Exercise 6.5 | Set 2