Bihar School Examination Board (BSEB) Class 8 Mathematics: Factorisation

Instructions. Answer all questions. Fill exactly one bubble per question on the OMR sheet.

1. Factorisation

   1.

   Factorise $12a^2b + 15ab^2$.

   1. (A)

      $3a(4ab + 5b^2)$

   2. (B)

      $3b(4a^2 + 5ab)$

   3. (C)

      $ab(12a + 15b)$

   4. (D)

      $3ab(4a + 5b)$

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   Answer: (D)

   $3ab(4a + 5b)$

   To factorise $12a^2b + 15ab^2$, find the greatest common factor (GCF) of the terms. The GCF of $12a^2b$ and $15ab^2$ is $3ab$. Dividing each term by $3ab$ gives $4a$ and $5b$ respectively, so the factorised form is $3ab(4a + 5b)$.

   Factorisation · Easy

2. 2.

   Factorise $x^2 + 8x + 16$.

   1. (A)

      $(x + 4)^2$

   2. (B)

      $(x + 4)(x - 4)$

   3. (C)

      $(x + 8)(x + 2)$

   4. (D)

      $(x - 4)^2$

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   Answer: (A)

   $(x + 4)^2$

   The expression $x^2 + 8x + 16$ is a perfect square trinomial because it matches the form $a^2 + 2ab + b^2$, where $a = x$ and $b = 4$. Thus, it factorises to $(x + 4)^2$.

   Factorisation · Medium

3. 3.

   Factorise $49p^2 - 36q^2$.

   1. (A)

      $(49p - 36q)(p + q)$

   2. (B)

      $(7p + 6q)^2$

   3. (C)

      $(7p - 6q)^2$

   4. (D)

      $(7p + 6q)(7p - 6q)$

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   Answer: (D)

   $(7p + 6q)(7p - 6q)$

   The expression $49p^2 - 36q^2$ is in the form of a difference of squares, $a^2 - b^2 = (a - b)(a + b)$. Here, $a = 7p$ and $b = 6q$. Therefore, the factorised form is $(7p + 6q)(7p - 6q)$.

   Factorisation · Medium

4. 4.

   Factorise $5x^2 - 20x$.

   1. (A)

      $5(x^2 - 4x)$

   2. (B)

      $5x(x - 4)$

   3. (C)

      $x(5x - 20)$

   4. (D)

      $5x(x + 4)$

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   Answer: (B)

   $5x(x - 4)$

   To factorise $5x^2 - 20x$, find the greatest common factor (GCF) of the terms. The GCF of $5x^2$ and $20x$ is $5x$. Dividing each term by $5x$ gives $x$ and $-4$ respectively, so the factorised form is $5x(x - 4)$.

   Factorisation · Easy

— End of the paper · updated 14 October 2026 —