Question

factorize 27x³ + 125y³ + 135x²

y + 225xy²​

Answer 1

Question :

• Factorize 27x³ + 125y³ + 135x²y + 225xy²

Given :

• Expression - 27x³ + 125y³ + 135x²y + 225xy²

To find :

• Factors of the expression.

Solution :

• Here, We are given with an expression and we are asked to find the factors of the expression. Let's Factorize the expression and find the factors.

According to the question,

⟶ 27x³ + 125y³ + 135x²y + 225xy²

★ (a + b)³ = a³ + b³ + 3a²b + 3ab²

Here,

• a = 3x
• b = 5y

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

⟶ (3x + 5y)³

Therefore, Factors obtained by factorising 27x³ + 125y³ + 135x²y + 225xy² are (3x + 5y)(3x + 5y)(3x + 5y).

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Let's verify :-

We can verify by Factorising the results "(3x + 5y)(3x + 5y)(3x + 5y)" if the left hand side will be equal to the right hand side then the factors obtained are correct.

⟶ (3x + 5y)(3x + 5y)(3x + 5y) = 27x³ + 125y³ + 135x²y + 225xy²

⟶ (3x)(3x)(3x) + (5y)(5y)(5y) + (3x)(9x)(5y) + (9x)(5y)(5y) = 27x³ + 125y³ + 135x²y + 225xy²

⟶ 27x³ + 125y³ + 135x²y + 225xy² = 27x³ + 125y³ + 135x²y + 225xy²

LHS = 27x³ + 125y³ + 135x²y + 225xy²

RHS = 27x³ + 125y³ + 135x²y + 225xy²

LHS = RHS

Hence, Verified!