NCERT Solutions for Class 8 Maths Chapter 12 Exercise 12.3 Factorisation in Hindi and English Medium updated for CBSE session 2024-25. All the questions of ex. 12.3 class 8th mathematics are revised according to new syllabus and latest NCERT books issued for CBSE 2024-25.

## 8th Maths Exercise 12.3 Solution in Hindi and English Medium

Class: 8 | Mathematics |

Chapter: 12 | Exercise: 12.3 |

Topic: | Factorisation |

Content: | NCERT Book Solutions |

Session: | CBSE 2024-25 |

Medium: | Hindi and English Medium |

### Class 8 Maths Chapter 12 Exercise 12.3 Solution

Class VIII Mathematics NCERT textbook Ex. 12.3 Factorisation updated for 2024-25 CBSE and state boards like MP board, UP board and other also. All the contents are prepared by subject experts using easier methods. Step by step solutions are given in PDF as well as videos solutions. Contact us if you are not getting solutions in videos or text, we here to help you.

#### Factorisation When Given Expression is Difference of Two Squares

FORMULA: (a – b)² = (a + b) (a – b)

**Factorise: (i) 49x² – 16y² (ii) 64 – x² (iii) y² – 121**

We have:

(i) 49x² – 16y²

= (7x)² – (4y)²

= (7x + 4y) (7x – 4y) {Applying formula (a – b)² = (a + b) (a – b)}

(ii) 64 – x²

= (8)² – (x)²

= (8 + x) (8 – x) {Applying formula (a – b)² = (a + b) (a – b)}

(iii) y² – 121

= (y)² – (11)²

= (y + 11) (y – 11) {Applying formula (a – b)² = (a + b) (a – b)}

**Factorise: 25 (x + y)² – 36 (x – 2y)²**

We have:

25 (x + y)² – 36 (x – 2y)²

= {5(x + y)}² – {6(x – 2y)}²

= {5 (x + y) + 6(x – 2y)} {5(x + y) – 6(x – 2y)}

{Applying formula (a – b)² = (a + b) (a – b)}

= (11x – 7y) (7y – x)

##### Factorisation When Expression is a Perfect Square (Using Identilies)

FORMULAE:

- a² + b² + 2ab = (a + b)²
- a² + b² – 2ab = (a – b)²

**Factorise: (i) x² + 10x + 25 (ii) x² – 20x + 100**

We have:

(i) x² + 10x + 25

= X2 + (5)² + 2 X x X 5 = (x + 5)² {By applying formula: a² + b² + 2ab = (a + b)²}

(ii) x² – 20x + 100

= x² + 10² – 2 X x X 10 = (x – 10)² {By applying formula: a² + b² – 2ab = (a – b)²}

**Factorise: 4x² + 9y² + 12xy**

We have:

4x² + 9y² + 12xy

= (2x)² + (3y)² + 2 X 2x X 3y

= (2x + 3y)²

**Factorise: x² + 8x + 16**

We have:

x² + 8x + 16

we can write this expression in the form of a² + b2 + 2ab

= x² + 4² + 2 X 4 X x

= (x + 2)²

**Factorise: p² – 10p + 25**

We have:

p² – 10p + 25 we can write this expression in the form of a² + b² – 2ab

= p² + 5² – 2 x p x 5

= (p – 5)² {By applying formula: a² + b² – 2ab = (a – b)²}

**Factorise: a⁴ + 25b⁴ – 10a² b²**

We can write this expression in the form of a² + b² – 2ab

= (a²)² + (5b²)² – 2 x a² x 5b²

= (a² – 5b²)²

{By applying formula: a² + b² – 2ab = (a – b)²}