Question

14. factorise :

125x³ - 27y³ - 225x²y + 135xy²​

Answer 1

Answer:

⇒ (5x + 3y)³

Step-by-step explanation:

Given :

To factorize :

125x³ + 225x²y + 135xy² + 27y³

Solution :

We know that,

⇒ (a + b)³ = a³ + 3a²b + 3ab² + b³

So,

⇒ 125x³ + 225x²y + 135xy² + 27y³

⇒ 5³ × x³ + 3 × 5² × x² × 3 × y + 3 × 5 × x × 3² × y² + 3³ × y³

⇒ (5x)³ + 3 × (5x)² × (3y) + 3 × (5x) × (3y)² + (3y)³

⇒ (5x)³ + 3(5x)²(3y) + 3(5x)(3y)² + (3y)³

Here a = 5x , b = 3y

⇒ (5x + 3y)³

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Answer 2

Answer:

⇒ (5x + 3y)³

Step-by-step explanation:

Given :

To factorize :

125x³ + 225x²y + 135xy² + 27y³

Solution :

We know that,

⇒ (a + b)³ = a³ + 3a²b + 3ab² + b³

So,

⇒ 125x³ + 225x²y + 135xy² + 27y³

⇒ 5³ × x³ + 3 × 5² × x² × 3 × y + 3 × 5 × x × 3² × y² + 3³ × y³

⇒ (5x)³ + 3 × (5x)² × (3y) + 3 × (5x) × (3y)² + (3y)³

⇒ (5x)³ + 3(5x)²(3y) + 3(5x)(3y)² + (3y)³

Here a = 5x , b = 3y

⇒ (5x + 3y)³