Question

Factorise: 54 a3 - 250b3

Answer 1

Answer:

Hey here's Ur solution..... hope it helps

Answer 2

Answer:

The factors of 54a³ - 250b³ are 2 (3a - 5b)(9a² + 15ab + 25b²).

Step-by-step explanation:

The equation can be factorized as follows:

$54a^{3}-250b^{3}\\=2(27a^{3}-125b^{3})\\=2[3^{3}\times a^{3})-(5^{3}\times b^{3})] \\=2[(3a)^{3}-(5b)^{3}]$

The expansion of (a³ - b³) is:

$(a^{3}-b^{3})=(a-b)(a^{2}+ab+b^{2})$

Use this relation and find the factors as follows:

$54a^{3}-250b^{3}=2[(3a)^{3}-(5b)^{3}]\\=2[(3a-5b)((3a)^{2}+(3a\times 5b)+(5b)^{2}]\\=2[(3a-5b)(9a^{2}+15ab+25b^{2})]$

Thus, the factors of 54a³ - 250b³ are 2 (3a - 5b)(9a² + 15ab + 25b²).