text: # BSE Odisha 8th Class Maths Solutions Algebra Chapter 4 ଉତ୍ପାଦକୀକରଣ Ex 4(b)
  
  Odisha State Board BSE Odisha 8th Class Maths Solutions Algebra Chapter 4 ଉତ୍ପାଦକୀକରଣ Ex 4(b) Textbook Exercise Questions and Answers.
  
  ## BSE Odisha Class 8 Maths Solutions Algebra Chapter 4 ଉତ୍ପାଦକୀକରଣ Ex 4(b)
  
  Question 1.
  x² + xy + 8x + 8y
  ଡ –
  x² + xy + 8x + 8yx(x + y) + 8(x + y)(x + y)(x + 8)
  
  Question 2.
  pq + pr + q² + qr
  ଡ –
  pq + pr + q² + qr = p(q + r) + q(q + r) = (q + r)(p + q)
  
  Question 3.
  ab+db+ac+dc
  ଡ –
  ab + db + ac + dc = b(a + d) + c(a + d) = (a+d)(b+c)
  
  Question 4.
  pq + qr + pr + r²
  ଡ –
  pq + qr + pr + r² = q(p + r) + r(p + r) = (p + r)(q + r)
  
  Question 5.
  15xy – 6x + 5y – 2
  ଡ –
  15xy – 6x + 5y – 2 = 3x(5y – 2)+ 1(5y – 2) = (5y – 2)(3x + 1)
  
  Question 6.
  ax + bx – ay – by
  ଡ –
  ax + bx – ay – by = x(a + b) – y(a + b) = (a + b)(x – y)
  
  Question 7.
  15pq + 15 + 9q + 25p
  ଡ –
  15Pq + 15 + 9q + 25p = 15pq + 9q + 25p + 15
  = 3q(5p + 3) + 5(5p + 3) = (5p + 3)(3q + 5)
  
  Question 8.
  2a + 6b – 3(a + 3b)²
  ଡ –
  2a + 6b – 3(a + 3b)² = 2(a + 3b) – 3(a + 3b)(a + 3b)
  
  Question 9.
  a² + 2a + ab + 2b
  ଡ –
  a² + 2a + ab + 2b = a(a + 2) + b(a + 2) = (a + 2)(a + b)
  
  Question 10.
  x² – xz + xy – yz
  ଡ –
  x² – xz + xy – yz = x(x – z) + y(x – z) = (x – z)(x + y)
  
  Question 11.
  a² + bc – ba – ac
  ଡ –
  a² + bc – ba – ac = a² – ba – ac + bc = a(a – b) – c(a – b) = (a – b) (a – c)
  
  Question 12.
  2p² – pq – 2pr + qr
  ଡ –
  2p² – q – 2pr + qr = p(2p – q) -r²(p – q) = (2p – q)(p – r²)
  
  Question 13.
  x² – 3x + 2x – 6
  ଡ –
  x² – 3x + 2x – 6 = x(x – 3) + 2(x – 3) = (x – 3)(x + 2)
  
  Question 14.
  2x² – 5x + 4x – 10
  ଡ –
  2x² – 5x + 4x – 10 = x(2x – 5) + 2(2x – 5) = (2x – 5)(x + 2)
  
  Question 15.
  x² – y² + x – xy²
  ଡ –
  x² – y² + x – xy² = x² + x – xy² – y² = x(x + 1) – y²(x + 1) = (x + 1)(x – y²)
  
  Question 16.
  lm² – mn² – lm + n²
  ଡ –
  lm² – mn² – lm + n² = lm² – lm – mn² + n²
  = lm(m – 1) – n(m – 1) = (m – 1) (lm – n²)
  
  Question 17.
  x³ – 2x²y + 3xy² – 6y³
  ଡ –
  x³ – 2x²y + 3xy² – 6y³ = x² (x – 2y) + 3y² (x – 2y) = (x – 2y) (x² + 3y²)
  
  Question 18.
  6ab – b² + 12ac – 2bc
  ଡ –
  6ab – b² + 12ac – 2bc = 6ab + 12ac – b² – 2bc
  =6a(b + 2c) – b(b + 2c) = (b + 2c)(6a – b)
  
  Question 19.
  x² – 11xy – x + 11y
  ଡ –
  x² – 11xy – x + 11y = x(x – 11y) – 1(x – 11y) = (x – 11y)(x – 1)
  
  Question 20.
  3ax – 6ay – 85y + 4bx
  ଡ –
  3ax – 6ay – 8by + 4bx = 3ax – 6ay + 4bx – 8by
  = 3a (x – 2y) + 4b(x – 2y) = (x – 2y) (3a + 4b)
explanation: The document is a set of solutions for algebraic factorization problems from a textbook exercise for 8th-grade students in Odisha, India. Each problem presents an algebraic expression and provides the factorized form as the answer.
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distilabel_metadata.content: # BSE Odisha 8th Class Maths Solutions Algebra Chapter 4 ଉତ୍ପାଦକୀକରଣ Ex 4(b)
  
  Odisha State Board BSE Odisha 8th Class Maths Solutions Algebra Chapter 4 ଉତ୍ପାଦକୀକରଣ Ex 4(b) Textbook Exercise Questions and Answers.
  
  ## BSE Odisha Class 8 Maths Solutions Algebra Chapter 4 ଉତ୍ପାଦକୀକରଣ Ex 4(b)
  
  Question 1.
  x² + xy + 8x + 8y
  ଡ –
  x² + xy + 8x + 8yx(x + y) + 8(x + y)(x + y)(x + 8)
  
  Question 2.
  pq + pr + q² + qr
  ଡ –
  pq + pr + q² + qr = p(q + r) + q(q + r) = (q + r)(p + q)
  
  Question 3.
  ab+db+ac+dc
  ଡ –
  ab + db + ac + dc = b(a + d) + c(a + d) = (a+d)(b+c)
  
  Question 4.
  pq + qr + pr + r²
  ଡ –
  pq + qr + pr + r² = q(p + r) + r(p + r) = (p + r)(q + r)
  
  Question 5.
  15xy – 6x + 5y – 2
  ଡ –
  15xy – 6x + 5y – 2 = 3x(5y – 2)+ 1(5y – 2) = (5y – 2)(3x + 1)
  
  Question 6.
  ax + bx – ay – by
  ଡ –
  ax + bx – ay – by = x(a + b) – y(a + b) = (a + b)(x – y)
  
  Question 7.
  15pq + 15 + 9q + 25p
  ଡ –
  15Pq + 15 + 9q + 25p = 15pq + 9q + 25p + 15
  = 3q(5p + 3) + 5(5p + 3) = (5p + 3)(3q + 5)
  
  Question 8.
  2a + 6b – 3(a + 3b)²
  ଡ –
  2a + 6b – 3(a + 3b)² = 2(a + 3b) – 3(a + 3b)(a + 3b)
  
  Question 9.
  a² + 2a + ab + 2b
  ଡ –
  a² + 2a + ab + 2b = a(a + 2) + b(a + 2) = (a + 2)(a + b)
  
  Question 10.
  x² – xz + xy – yz
  ଡ –
  x² – xz + xy – yz = x(x – z) + y(x – z) = (x – z)(x + y)
  
  Question 11.
  a² + bc – ba – ac
  ଡ –
  a² + bc – ba – ac = a² – ba – ac + bc = a(a – b) – c(a – b) = (a – b) (a – c)
  
  Question 12.
  2p² – pq – 2pr + qr
  ଡ –
  2p² – q – 2pr + qr = p(2p – q) -r²(p – q) = (2p – q)(p – r²)
  
  Question 13.
  x² – 3x + 2x – 6
  ଡ –
  x² – 3x + 2x – 6 = x(x – 3) + 2(x – 3) = (x – 3)(x + 2)
  
  Question 14.
  2x² – 5x + 4x – 10
  ଡ –
  2x² – 5x + 4x – 10 = x(2x – 5) + 2(2x – 5) = (2x – 5)(x + 2)
  
  Question 15.
  x² – y² + x – xy²
  ଡ –
  x² – y² + x – xy² = x² + x – xy² – y² = x(x + 1) – y²(x + 1) = (x + 1)(x – y²)
  
  Question 16.
  lm² – mn² – lm + n²
  ଡ –
  lm² – mn² – lm + n² = lm² – lm – mn² + n²
  = lm(m – 1) – n(m – 1) = (m – 1) (lm – n²)
  
  Question 17.
  x³ – 2x²y + 3xy² – 6y³
  ଡ –
  x³ – 2x²y + 3xy² – 6y³ = x² (x – 2y) + 3y² (x – 2y) = (x – 2y) (x² + 3y²)
  
  Question 18.
  6ab – b² + 12ac – 2bc
  ଡ –
  6ab – b² + 12ac – 2bc = 6ab + 12ac – b² – 2bc
  =6a(b + 2c) – b(b + 2c) = (b + 2c)(6a – b)
  
  Question 19.
  x² – 11xy – x + 11y
  ଡ –
  x² – 11xy – x + 11y = x(x – 11y) – 1(x – 11y) = (x – 11y)(x – 1)
  
  Question 20.
  3ax – 6ay – 85y + 4bx
  ଡ –
  3ax – 6ay – 8by + 4bx = 3ax – 6ay + 4bx – 8by
  = 3a (x – 2y) + 4b(x – 2y) = (x – 2y) (3a + 4b)
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document is a set of solutions for algebraic factorization problems from a textbook exercise for 8th-grade students in Odisha, India. Each problem presents an algebraic expression and provides the factorized form as the answer.
  
  Label: multiple-question-and-answer