Question

only ques.9 pls




pls​

Answer 1

QUESTION:

• Factorize :- (a² - b²)³ + (b² - c²)³ + (c² - a²)³

ANSWER:

• 3(a² - b²)(b² - c²)(c² - a²)

GIVEN:

• (a² - b²)³ + (b² - c²)³ + (c² - a²)³

TO:

• Factorize :- (a² - b²)³ + (b² - c²)³ + (c² - a²)³

ALGEBRAIC IDENTITY:

$\bf{\boxed{ {x}^{3} + {y}^{3} + { z}^{3} = 3xyz[when \: \: x + y + z = 0]}}$

EXPLANATION:

Take

• x = (a² - b²)
• y = (b² - c²)
• z = (c² - a²)

x + y + z = (a² - b²+ b² - c² + c² - a²) = 0

(a² - b²)³ + (b² - c²)³ + (c² - a²)³ = 3(a² - b²)(b² - c²)(c² - a²)

HENCE 3(a² - b²)(b² - c²)(c² - a²) IS THE FINAL ANSWER.

SOME MORE IDENTITIES:

$\boxed{\begin{minipage}{5 cm} {(x + y)}^{2} = {x}^{2} + 2xy + {y}^{2} \\ \\ {(x - y)}^{2} = {x}^{2} - 2xy + {y}^{2} \\ \\ (x + y)(x - y) = {x}^{2} - {y}^{2} \\ \\ {(x - y)}^{3} = (x - y)( {x}^{2} + xy + {y}^{2} ) \\ \\{(x + y)}^{3} = (x + y)( {x}^{2} - xy + {y}^{2} ) \end{minipage}}$

Answer 2

Answer:

Take

x = (a² - b²)

y = (b² - c²)

z = (c² - a²)

x + y + z = (a² - b²+ b² - c² + c² - a²) = 0

(a² - b²)³ + (b² - c²)³ + (c² - a²)³ = 3(a² - b²)(b² - c²)(c² - a²)

HENCE 3(a² - b²)(b² - c²)(c² - a²) IS THE FINAL ANSWER.