Question

plz guyz ❤❤❤
simplify

27x cube+y cube-z cube -9 xyz

2 root 2 a cube +3 root 3 b cube +c cube -3 root 6 abc


plz solve both

Answer 1

( 1 ). 27x³ + y³ + z³ - 9xyz

(3x)³ + (y)³ + (z)³ - (3)(3x)(y)(z)

(3x + y + z)(9x² + y² + z² - 3xy - yz - 3xz)
$\bold{\to\to\to\to\to\to\to\to\to\to\boxed{ a^3 +b^3 + c^3-3abc = (a+b+c)(a^2 + b^2+c^2-ab-bc-ca)}}$

( 2 ). 2√2a³ + 3√3b³ + c³ - 3√6abc

(√2a)³ + (√3b)³ + (c)³ - 3(√2a)(√3b)(c)

(√2a + √3b + c)(2a² + 3b² + c² - √6ab - √3bc - √2ac)
$\bold{\to\to\to\to\to\to\to\to\to\to\boxed{ a^3 +b^3 + c^3-3abc = (a+b+c)(a^2 + b^2+c^2-ab-bc-ca)}}$

Answer 2

✴✴$\bold{Hey \: friend}$✴✴
--------------------------------------------------------
✴✴$\underline{ Here \: is \: your \: answer↓}$

⬇⬇⬇⬇⬇⬇⬇⬇⬇⬇⬇⬇⬇⬇

▶⏩ In both questions same identity is used that is:-)

↪➡$\boxed{ {a}^{3} + {b}^{3} + {c}^{3} - 3abc \: = \: (a + b + c)( {a}^{2} + {b}^{2} + {c}^{2} - ab - bc - ca.}$

▶⏩ 1st question:-)

↪➡$\bold{ \: {27x}^{3} + {y}^{3} + {( - z)}^{3} - 9xyz}$
$\bf{ = {(3x)}^{3} + {y}^{3} + {( - z)}^{3} - 3 \times (3x) \times y \times z}$

↪➡$\bf{(3x + y + ( - z))( \: {(3x)}^{2} + {y}^{2} + {( - z)}^{2} - (3x)y - y( - z) - ( - z)(3x)}$

↪➡$\bf{(3x + y - z) \: ( {9x}^{2} + {y}^{2} + {z}^{2} - 3xy + yz + 3xz}$

✅✅ Hence, 1st question is factorised.✔✔

▶⏩ 2nd question:-)

↪➡$\bf{2 \sqrt{2} {a}^{3} + 3 \sqrt{3} {b}^{3} + {c}^{3} - 3 \sqrt{6}abc}$

↪➡$\bf{ ( \sqrt{2} {a})^{3} + ( \sqrt{3} {b})^{3} + {c}^{3} - 3 \sqrt{2}a \sqrt{3}bc}$

↪➡$\bf{ ( \sqrt{2}a + \sqrt{3}b + c) \: ( \: ({ \sqrt{2}a })^{2} + ({ \sqrt{3}b })^{2} + ({c})^{2} - ( \sqrt{2}a) (\sqrt{3}b) - ( \sqrt{3}b)(c) - (c)( \sqrt{2}a)}$

↪➡$\bf{ ( \sqrt{2}a + \sqrt{3}b + c) \: (2 {a}^{2} + 3 {b}^{2} + {c}^{2} - \sqrt{6}ab - \sqrt{3}bc - \sqrt{2}ca)}$

✔✔ Hence, 2nd question is factorised ✅✅.

$\boxed{THANKS}$

$\underline{Hope \: it \: is \: helpful \: for \: you}$