Question

Q.11 Factorize the following by using a suitable identity: (a) a^3 +b^3 – 8c^3 + 6abc. if you give correct answer means i will mark you as brainlist

Answer 1

Step-by-step explanation:

${a}^{3} + {b}^{3} - {8c}^{3} + 6abc$

$= {(a)}^{3} + {(b)}^{3} + {( - 2c)}^{3} - 3(a)(b)( - 2c)$

using the identity

${a}^{3} + {b}^{3} + {c}^{3} - 3abc = (a + b + c)( {a}^{2} + {b}^{2} + {c}^{2} - ab - bc - ca)$

here, a=a, b=b, c=-2c

$(a + b + ( - 2c))( {a}^{2} + {b}^{2} + {( - 2c)}^{2} - (a)(b) - (b)( - 2c) - ( - 2c)(a))$

$= (a + b - 2c)( {a}^{2} + {b}^{2} + {4c}^{2} - ab + 2bc + 2ca$

Answer 2

Answer:

(a + b - 2c)(a² + b² + 4c² - ab + 2bc + 2ca)

Step-by-step explanation:

a^3 + b^3 - 8c^3 + 6abc

⇒ a³ + b³ + (-2c)³ - 3ab(-2c)

[∴ a³ + b³ + c³- 3abc = (a + b + c)(a² + b² + c²- ab - bc - ca) ]

⇒ (a + b + (-2c))(a² + b² + (-2c)² - ab - b(-2c) - (-2c)a)

⇒ (a + b - 2c)(a² + b² + 4c² - ab + 2bc + 2ca)

Hope it helps!