CG Board Class 8 Mathematics Chapter 4 Solutions: Multiplication and Division of Algebraic Expressions (बीजीय व्यंजकों का गुणा एवं भाग) – 2026-27

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CG SCERT (Chhattisgarh Board) Class 8 Mathematics Solutions | 2026-27 Official Edition

Complete 100% textbook-grounded CG Board Class 8 Mathematics Chapter 4 Solutions: Multiplication and Division of Algebraic Expressions (बीजीय व्यंजकों का गुणा एवं भाग) in Bilingual Format (English & Hindi Medium).

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Question 1

Multiply the given expressions to each other


📝 Question:

Multiply the given expressions to each other

💡 Solution:

(i) (2x + 7)(3x + 2)**

  • (ii) (3x – 5)(2x + 9)
  • (iii) (7x – 6)(15x – 2)
  • (iv) (1/2x + 5y)(3x – 6/5y)
  • (v) (x + 5y)(7x – y)

Question 2

Find the values


📝 Question:

Find the values

💡 Solution:

(i) (2x + 3y)(3x + 2y) + (x + y)(y + x)**

  • (ii) (2x + 1/2)(3x/2 – 1/4)
  • (iii) (x2 + y2)(3x – 5y)
  • (iv) (a + b)(a + b)

Question 3

Multiply x y and 3x 4y to each…


📝 Question:

Multiply (x + y) and (3x + 4y) to each other and verify the product for the following values

💡 Solution:

(i) x = 2, y = -1**

(ii) x = 1, y = 0

  • (i) Verification for x = 2, y = -1:
  • (ii) Verification for x = 1, y = 0:

Question 1

Find the values


📝 Question:

Find the values

💡 Solution:

(i) 18x2y ÷ (-6xy)**

-3x

  • (ii) -15x3y2z ÷ (-5x2yz)

3xy

  • (iii) -5x5y7 ÷ (-5x4y5)

+xy2

  • (iv) 32a4b2c ÷ (-8abc)

-4a3b

  • (v) -28a4b6c8 ÷ 7a2b4c6

-4a2b2c2

Question 2

Divide


📝 Question:

Divide

💡 Solution:

(i) (2x4 – 6x3 + 4x2) ÷ 2x2**

x2 - 3x + 2

  • (ii) (5a4b3 – 10a3b2 + 15a2b2) ÷ (-5a2b2)

-a2b + 2a - 3

  • (iii) (27a4 – 36a2) ÷ (-9a)

-3a3 + 4a

  • (iv) (x4 + 2x3 + 2x2) ÷ 4x2

1/4 x2 + 1/2 x + 1/2

  • (v) (a2 + ab + ac) ÷ a

a + b + c

Question 1

Write the given polynomial in the decreasing order…


📝 Question:

Write the given polynomial in the decreasing order of the variables

💡 Solution:

(i) 15x2 + 3x4 – 8x – 4x3 – 15**

3x4 - 4x3 + 15x2 - 8x - 15

  • (ii) 12m5 – 9m3 + 16 – 6m2 + 8m

12m5 - 9m3 - 6m2 + 8m + 16

  • (iii) 9m4 – 16m2 + 4m – m3 + 16

9m4 - m3 - 16m2 + 4m + 16

  • (iv) 4 – 8y3 + 12y4 – 6y2

12y4 - 8y3 - 6y2 + 4

Question 2

Divide and say whether the divisor is a…


📝 Question:

Divide and say whether the divisor is a multiple factor of the dividend

💡 Solution:

(i) (x2 – 11x + 30) ÷ (x – 5)**

  • (ii) (x2 + 20x + 91) ÷ (x + 7)
  • (iii) (x2 – 5x – 6) ÷ (x – 6)
  • (iv) (x3 – 5x2 – 2x + 24) ÷ (x – 4)
  • (v) (a2 + 2ab + b2) ÷ (a + b)

Question 3

Divide and prove that the divisor and dividend…


📝 Question:

Divide and prove that the divisor and dividend are not multiple factors. Write down the quotient and remainder

💡 Solution:

(i) (x3 + 2x2 + 3x + 4) ÷ (x – 1)**

Quotient = x2 + 3x + 6, remainder = 10

  • (ii) (x3 + 3x2 – 4x – 12) ÷ (x + 5)

Quotient = x2 - 2x + 6, remainder = -42

  • (iii) (2x4 – 4x3 + 10x2 – 13x + 6) ÷ (x – 3)

Quotient = 2x3 - 4x2 + x + 5, remainder = -21

  • (iv) (2x3 – 4x2 + 5x + 9) ÷ (x – 1)

Quotient = 2x2 - 2x + 3, remainder = 12

Question 4

Divide and verify Dividend Divisor Quotient Remainder


📝 Question:

Divide and verify: Dividend = Divisor × Quotient + Remainder

💡 Solution:

(i) (m2 – 3m + 7) ÷ (m – 2)**

Quotient = m - 1, remainder = 5

  • (ii) (a3 – 2a2 + a + 2) ÷ (a + 2)

Quotient = a2 - 4a + 9, remainder = -16

  • (iii) (3x3 + x2 – 7x + 9) ÷ (x – 1)

Quotient = 3x2 + 4x - 3, remainder = +6

  • (iv) (2x3 + 3x2 + 7x + 15) ÷ (x2 + 4)

Quotient = 2x + 3, remainder = -x + 3

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