Question

64 ka m cube _343 ka n cube

Answer 1

Answer:

(4m - 7n)(16m² + 28n + 49n²)

Step-by-step explanation:

64m³ - 343n³

It can be written as ;

(4m)³ - (7n)³

Using identity here ;

a³ - b³ = (a - b) (a² + ab + b²)

⇒ (4m)³ - (7n)³

⇒ (4m - 7n) {(4m)² + 4m * 7n + (7n)²}

⇒ (4m - 7n)(16m² + 28n + 49n²)

Hence, the answer is (4m - 7n)(16m² + 28n + 49n²).

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While solving this kind of question, always remember that identity should be used properly. Some of the algebraic identities are given below :

1. (a + b)² = a² + 2ab + b²
2. (a - b)² = a² - 2ab + b²
3. (a + b)³ = a³ + b³ + 3ab (a + b)
4. (a - b)³ = a³ - b³ - 3ab (a - b)
5. a³ + b³ = (a + b)(a² - 2ab + b²)
6. a³ - b³ = (a - b)(a² + 2ab + b²)