Question

factorise the following

Answer 1

1/
Solution:

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Given:

To factorize:

125x³ - 27y³ - 225x²y + 135xy²

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We can also write the expression as,

125x³ - 225x²y + 135xy² - 27y³


= (5x)³ - 3(5x)(5x)(3y) + 3(5x)(3y)(3y) - (3y)³


=(5x)³ - 3(5x)²(3y) + 3(5x)(3y)² - (3y)³


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As we know the identity,

that,.

(a-b)³ = a³-3a²b+3ab²-b³

hence,

a = 5x,

b = 3y,

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

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2/

Solution:

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Given:

To factorize:

   $\frac{64}{125}a^3 - \frac{96}{25}a^2 + \frac{48}{5}a-8$

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We can also write the given expression as,


$\frac{64a^3}{125} - \frac{96a^2}{25} + \frac{48a}{5}-8$


= $( \frac{4a}{5})^3 - 3( \frac{4a}{5})( \frac{4a}{5} )(2) + 3(\frac{4a}{5})(2)(2) +(2)^3$


=$( \frac{4a}{5} )^3 -3( \frac{4a}{5} )^2(2) + 3( \frac{4a}{5} )(2)^2 +(2)^3$


As we know the identity that,

(a-b)³ = a³ - 3a²b+ 3ab² -b³

where,

a = $\frac{4a}{5}$

b = 2,.

$\frac{64}{125}a^3 - \frac{96}{25}a^2 + \frac{48}{5}a-8$ =($\frac{4a}{5} - 2$)³

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                             Hope it Helps !!