Important Questions Class 8 Maths Chapter 14 Factorization

Important questions for Class 8 Maths Chapter 14 factorization provided here with solutions. The questions are prepared as per Class 8 Maths CBSE syllabus (2022-2023) and the latest exam pattern. These questions cover various short answer type questions, long answer type questions and HOTS (High Order Thinking Skills) questions. These factorization extra questions will help CBSE students to be well-prepared for the Class 8 exam. Here, some important questions related to factorization topic from the NCERT Class 8 book are also included.

Also Check:

• Important 2 Marks Questions for CBSE 8th Maths
• Important 3 Marks Questions for CBSE 8th Maths
• Important 4 Marks Questions for CBSE 8th Maths

Factorization Important Questions For Class 8 (Chapter 14)

Some extremely important Class 8 questions from Chapter 14 i.e. factorization are provided below. Go through these factorization problems for better practice.

Short Answer Type Questions:

1. Express the following as in the form of (a+b)(a-b)

(i) a² – 64

(ii) 20a² – 45b²

(iii) 32x²y² – 8

(iv) x² – 2xy + y² – z²

(v) 49x² – 1

Solution:

For representing the expressions in (a+b)(a-b) form, use the following formula

a² – b² = (a+b)(a-b)

(i) a² – 64 = a² – 8² = (a + 8)(a – 8)

(ii) 20a² – 45b² = 5(4a² – 9b²) = 5(2a + 3b)(2a – 3b)

(iii) 32x²y² – 8 = 8( 4x²y² – 1) = 8(2xy + 1)(2xy – 1)

(iv) x² – 2xy + y² – z² = (x – y)² – z² = (x – y – z)(x – y + z)

(v) 49x² – 1 = (7x)² – (1)² = (7x + 1)(7x – 1)

2. Verify whether the following equations are correct. Rewrite the incorrect equations correctly.

(i) (a + 6)² = a² + 12a + 36

(ii) (2a)² + 5a = 4a + 5a

Solution:

(i) (a + 6)² = a² + 12a + 36

Here, LHS = (a + 6)² = a² + 12a + 36

Now, RHS = a² + 12a + 36

Hence, LHS = RHS.

(ii) (2a)² + 5a = 4a + 5a

Here, LHS = (2a)² + 5a = 4a² + 5a

Now, RHS = 4a + 5a

So, LHS ≠ RHS

Correct equation: (2a)² + 5a = 4a² + 5a

3. For a = 3, simplify a² + 5a + 4 and a² – 5a

Solution:

Substitute the value of a = 3 in the given equations.

a² + 5a + 4 = 3² + 5(3) + 4 = 9 + 15 + 4 = 28

And,

a² – 5a = 3² – 5(3) = 9 – 15 = -6

Long Answer Type Questions:

4. Find the common factors of the following:

(i) 6 xyz, 24 xy² and 12 x²y

(ii) 3x² y³, 10x³ y² and 6x² y² z

Solution:

(i) 6 xyz = 2 × 3 × x × y × z

24 xy² = 2 × 2 × 2 × 3 × x × y × y

12 x²y = 2 × 2 × 3 × x × x × y

Thus, the common factors are common factors of 6 xyz, 24 xy² and 12 x²y are 2, 3, x, y and, (2 × 3 × x × y) = 6xy

(ii) 3x² y³ = 3 × x × x × y × y × y

10x³ y² = 2 × 5 × x × x × x × y × y

6 x² y² z = 3 × 2 × x × x × y × y × z

Now, the common factors of 3x² y³, 10x³ y² and 6x² y² z are x², y² and, (x² × y²) = x² y²

5. Factorize the following expressions:

(i) 54x³y + 81x⁴y²

(ii) 14(3x – 5y)³ + 7(3x – 5y)²

(iii) 15xy + 15 + 9y + 25x

Solution:

(i) 54x³y + 81x⁴y²

= 2 × 3 × 3 × 3 × x × x × x × y + 3 × 3 × 3 × 3 × x × x × x × x × y × y

= 3 × 3 × 3 × x × x × x × y × (2 + 3 xy)

= 27x³y (2 + 3 xy)

(ii) 14(3x – 5y)³ + 7(3x – 5y)²

= 7(3x – 5y)² [2(3x – 5y) +1]

= 7(3x – 5y)² (6x – 10y + 1)

(iii) 15xy + 15 + 9y + 25x

Rearrange the terms as:

15xy + 25x + 9y + 15

= 5x(3y + 5) + 3(3y + 5)

Or, (5x + 3)(3y + 5)

6. Factorize (x + y)² – 4xy

Solution:

To solve this expression, expand (x + y)²

Use the formula:

(x + y)² = x² + 2xy + y²

(x + y)² – 4xy = x² + 2xy + y² – 4xy

= x² + y² – 2xy

We know, (x – y)² = x² + y² – 2xy

So, factorization of (x + y)² – 4xy = (x – y)²

7. Factorize x² + 6x – 16

Solution:

To factorize, it should be checked that the sum of factors of 16 should be equal to 6.

Here, 16 = -2 × 8 and 8 + (-2) = 6

So,

x² + 6x – 16 = x² – 2x + 8x – 16

= x(x – 2) + 8(x – 2)

= (x + 8) (x – 2)

Hence, x² + 6x – 16 = (x + 8) (x – 2)

8. Solve for (4x² – 100) ÷ 6(x + 5)

Solution:

= ⅔ (x – 5)

Class 8 Maths Chapter 14 Extra Questions

1. Factorise:
   (а) 14m⁵n⁴p² – 42m⁷n³p⁷ – 70m⁶n⁴p³
   (b) 2a²(b² – c²) + b²(2c² – 2a²) + 2c²(a² – b²)
2.  The area of a rectangle is 6a² + 36a and 36a width. Find the length of the rectangle.
3. What are the common factors of the following terms?
   (a) 25x²y, 30xy²
   (b) 63m³n, 54mn⁴

Topics Related to Class 8 Factorization

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