Question

8a^3+27b^3+125c^3-90abc​

Answer 1

$\red {\huge {\underline{ \frak{Your \: answEr : }}}}$

$\implies \tt{8 {a}^{3} + 27 {b}^{3} + 125 {c}^{3} - 90abc}$

$\implies \tt{ {(2a)}^{3} + {(3b)}^{3} + {(5c)}^{3} - 3 \times 2a \times 3b \times 5c }$

$\scriptsize\blacksquare \: \bold{ {a}^{3} + {b}^{3} + {c}^{3} - 3abc = (a + b + c)( {a}^{2} + {b}^{2} + {c}^{2} - ab - bc - ca) }$

$\blacksquare \: \boxed{ \frak {plugging \: values}}$

$\purple{\implies \tt{(2a + 3b + 5c)(4 {a}^{2} + 9 {b}^{2} + 25 {c}^{2} - 6ab - 15bc - 10ac) } }$

$\huge{\red{\ddot{\smile}}}$

Answer 2

Step-by-step explanation:

$\bf{\huge\mathcal{\boxed{\rm{\mathfrak\blue{Hey Mate:}}}}}$

8a³+27b³+125c³-90abc

= (2a)³ + (3b)³ + (5c)³ -3(2a)(3b)(5c)

We know that :

a³ + b³ + c³ - 3abc = (a+b+c)(a²+b²+c²-ab-bc-ac)

So, 8a³+27b³+125c³-90abc = (2a+3b+5c)(4a² + 9b² + 25c²-6ab-15bc−10ac)