Question

$Factories \: The \: Given \: Expression...$
$Solve \: This \: \: If \: \: You \: \: Know...\ \textless \ br /\ \textgreater$

$Note:- \\ \ \textless \ br /\ \textgreater \ No \: Spamming \\ \ \textless \ br /\ \textgreater \ Only \: Content \: Quality \: Answer..$
​

Answer 1

Answer:

Question:-

$\mathtt{Factorise}$

$\mathtt{ 125 - {8x}^{3} - 27 {y}^{3} - 90xy }$

Formula used:-

$\mathtt{ {x}^{3} + {y}^{3} + {z}^{3} = (x + y + z)( {x}^{2} + {y}^{2} + {z}^{2} - xy - yz - zx) }$

Solution:-

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

$\mathtt{ {x}^{3} + {y}^{3} + {z}^{3} = (x + y + z)( {x}^{2} + {y}^{2} + {z}^{2} - xy - yz - zx) }$

$\mathtt{ = 5 + ( - 2xy ) + ( - 3y)( {5 + {4}^{2} + {9y}^{2} + 10x - 6xy + 15y } }$

$\mathtt{ = (5 - 2x - 3y)(25 + {4x}^{2} + {9y}^{2} + 10x - 6xy + 15y)}$

Step-by-step explanation:

Hope this helps you.

# By Sparkly Princess

please swipe the ans to right also to see remaining part because it show only half.

Answer 2

Answer:

$\: \mathtt{Factorise} \\ \mathtt{ 125 - {8x}^{3} - 27 {y}^{3} - 90xy } \\ Formula \: used:- \\ \mathtt{ {x}^{3} + {y}^{3} + {z}^{3} = (x + y + z)( {x}^{2} + {y}^{2} + {z}^{2} - xy - yz - zx) } \\ Solution:- \\ \mathtt{ = {5}^{3} + {( - 2x)}^{3} + {( - 3y)}^{3} - 3(5)( - 2x)( - 3y) } \\ \mathtt{ {x}^{3} + {y}^{3} + {z}^{3} = (x + y + z)( {x}^{2} + {y}^{2} + {z}^{2} - xy - yz - zx) } \\ \mathtt{ = 5 + ( - 2xy ) + ( - 3y)( {5 + {4}^{2} + {9y}^{2} + 10x - 6xy + 15y } } \\ \mathtt{ = (5 - 2x - 3y)(25 + {4x}^{2} + {9y}^{2} + 10x - 6xy + 15y)}$

Hope it's helpful to you :) :)