14. factorise :
125x³ - 27y³ - 225x²y + 135xy²
Answers
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:
⇒ (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