Question

3√3x^3 - 5√5y^3 factorize

Answer 1

=(√3x)³-(√5y)³=(√3-√5){(√3)²+√3√5+(√5)²}=(√3-√5)(8+√15)

Answer 2

Answer:

Step-by-step explanation:

Concept:

Any other second number must be entirely divided by the first number, leaving no residue, for a number to be stated to be a factor of any other second number. Simply put, if a number (dividend) can be divided exactly by any other number (divisor), then the divisor is a factor of the dividend. The number itself and the common factor of one are shared by all numbers.

The term "prime number" refers to any natural number that only contains two elements, namely $1$and the number itself. An example of a prime number with just two factors, namely $1 and 2$, is $2$.

Given:

$3\sqrt{3}x^{3} - 5\sqrt{5} y^{3}$

Find:

To factorize the given $3\sqrt{3} x^{3} - 5\sqrt{5} y^{3}$

Solution:

Given number $3\sqrt{3} x^{3} - 5\sqrt{5} y^{3}$

So , we write $3$ as $\sqrt{3} * \sqrt{3}$ and $5$ as $\sqrt{5} * \sqrt{5}$

Then we will get

$\sqrt{3} * \sqrt{3} * \sqrt{3} x^{3} - \sqrt{5} * \sqrt{5} * \sqrt{5} y^{3}$

$(\sqrt{3x}) ^{3} - (\sqrt{5y})^{3}$

By using the formula $(a^{3} - b^{3} ) = (a - b) (a^{2} + b^{2} +ab )$

$=$ $(\sqrt{3x} - \sqrt{5y} ) ((\sqrt{3x})^{2} + (\sqrt{5y})^{2} + \sqrt{3x} * \sqrt{5y} )$

$= (\sqrt{3x} - \sqrt{5y}) (3x^{2} + 5x^{2} + \sqrt{15xy} )$

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