Question

X power 4 - (y + z) power 4

Answer 1

Answer:

( x + y + z ) ( x - y - z ) {x² + ( y + z )²}

Step-by-step explanation:

Given---> x⁴ - ( y + z )⁴

To find---> Factors of given expression

Solution---> We know that,

a² - b² = ( a + b ) ( a - b )

And a law of exponent

( aᵐ )ⁿ = aᵐⁿ

Now returning to original problem and applying above identity and law here , we get,

x⁴ - ( y + z )⁴ = ( x² )² - { ( y + z )² }²

= { x² + ( y + z )² } { x² - ( y + z )² }

= { x² + ( y + z )² } { x + ( y + z ) } { x - ( y + z ) }

= { x² + ( y + z )² } ( x + y + z ) ( x - y - z )

= ( x + y + z ) ( x - y - z ) { x² + ( y + z )² }

Additional identities--->

1) ( a + b )² = a² + b² + 2ab

2) ( a - b )² = a² + b² - 2ab

3) ( a + b )³ = a³ + b³ + 3ab ( a + b )

4) ( a - b )³ = a³ - b³ - 3ab ( a - b )

5) a³ + b³ = ( a + b ) ( a² + b² - ab )

6) a³ - b³ = ( a - b ) ( a² + b² + ab )

#Answerwithquality&#BAL

Answer 2

Answer:

Step-by-step explanation:

x^4-(x-z)^4 is the given expression

let (x-z) = y

So, x^4 - y^4 = (x²)² - (y²)² = {(x²) + (y²)} {(x²) - (y²)} = {(x²) + (y²)} (x+y) (x-y)

Put the value of y into the found expression

= {(x²) + (y²)} (x+y) (x-y)

= {x²+(x-z)²} (x+x-z) (x-x+z)

= (x²+x²+z²-2xz) (2x-z) (z)

= (2x²+z²-2xz) (2x-z)(z)

$ALWAY_SSMIL_E$  ^_^