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

  • Last Updated : 07 Apr, 2021

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 + 10x44x3 – 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

Attention reader! Don’t stop learning now. Participate in the Scholorship Test for First-Step-to-DSA Course for Class 9 to 12 students.




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