Question

X^4-(y+z)^4 factorise the above

Answer 1

Answer:

[ x² + y² + z² + 2yz ] [ x + y + z ] [ x - y - z ]

Step-by-step explanation:

Given : x⁴ - (y + z)⁴

We can write this as :

➾ (x²)² - [(y + z)²]²

Identity : a² - b² = (a + b)(a - b)

Here, a = x², b = (y + z)²

➾ [ x² + (y + z)² ] [ x² - (y + z)² ]

➾ [ x² + (y + z)² ] [ x² - (y + z)² ]

We can write this as :

➾ [ x² + (y + z)² ] [ (x)² - (y + z)² ]

Identity : a² - b² = (a + b)(a - b)

Here, a = x, b = y + z

➾ [ x² + (y + z)² ] [ (x) + (y + z) ] [ (x) - (y + z) ]

➾ [ x² + (y + z)² ] [ x + y + z ] [ x - y - z ]

➾ [ x² + (y + z)² ] [ x + y + z ] [ x - y - z ]

Identity : (a + b)² = a² + b² + 2ab

Here, a = y, b = z

➾ [ x² + (y)² + (z)² + 2(y)(z) ] [ x + y + z ] [ x - y - z ]

➾ [ x² + y² + z² + 2yz ] [ x + y + z ] [ x - y - z ]

Answer 2

❥${\red{\underline{\underline{\huge{\mathtt{Question:-}}}}}}$

x⁴ - (y+z)⁴ [ factorise]

❥${\red{\underline{\underline{\huge{\mathtt{Solution:-}}}}}}$

x⁴ - (y+z)⁴

[ We can write it (x²)² - {(y+z)²}²]

→ (x²)² - {(y+z)²}²

[ Apply a² - b² = (a+b)(a-b)]

→{x² + (y+z)²} {x² - (y+z)²}

[ Apply ★(a+b)² =a²+b²+2ab ★ a² - b² = (a+b)(a-b)]

→(x²+y²+z²+2yz) (x+y+z)(x-y-z)

❥${\red{\underline{\underline{\huge{\mathtt{Answer:-}}}}}}$

(x²+y²+z²+2yz) (x+y+z)(x-y-z)