Factorisation using identities

Chapter 14 Class 8 Factorisation
Concept wise

We know the identities

Let’s factorise using these identities

### x 2 + 4x + 4

x 2 + 4x + 4

= x 2 + 4 + 4x

= x 2 + (2) 2 + 2 × 2 × x

Using (a + b) 2 = a 2 + b 2 + 2ab

Where a = x , b = 2

= (x + 2) 2

### 4x 2 + 12x + 9

4x 2 + 12x + 9

= 4x 2 + 9 + 12x

= (2x) 2 + 3 2 + 2 × 2x × 3

Using (a+b) 2 = a 2 + b 2 + 2ab

Where a = 2x, b = 3

= (2 x + 3 ) 2

### x 2 − 4x + 4

x 2 – 4x + 4

= x 2 + 4 – 4x

= x 2 + (2) 2 – 2 × 2 × x

Using (a - b) 2 = a 2 + b 2 – 2ab

Where a = x, b = 2

= (x - 2) 2

### 4x 2 – 12x + 9

4x 2 – 12x + 9

= 4x 2 + 9 – 12x

= (2x) 2 + 3 2 – 2 × 2x × 3

Using (a - b) 2 = a 2 + b 2 – 2ab

Where a = 2x, b = 3

= (2 x - 3 ) 2

### 4x 2 − 9

4x 2 − 9

= (2x) 2 − 3 2

Using a 2 - b 2 = (a - b)  (a + b)

Where a = 2x, b = 3

= (2𝑥 − 3) (2𝑥 + 3)

### y 4 − 16

y 4 − 16

= (y 2 ) 2 − (4) 2

Using a 2 - b 2 = (a - b) (a + b)

Where a = y 2 , b = 4

= (y 2 - 4) (y 2 + 4)

= (y 2 - 2 2 ) (y 2 + 4)

Using a 2 - b 2 = (a - b)  (a + b)

Where a = y 2 , b = 4

= (y − 2) (y + 2) (y 2 + 4)

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