Question

simplify the following (2x-z)^3 + (2x+z)^3​

Answer 1

Answer:

4x ( 4 x² + 3 z² )

Step-by-step explanation:

To find--->

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( 2 x - z )³ + ( 2x + z )³ = ?

Solution --->

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We know that

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

= a³ - b³ - 3 a² b + 3 a b²

( a + b )³ = a³ + b³ + 3 a b ( a + b)

= a³ + b³ + 3a²b + 3ab²

Now

(a - b )³ + ( a + b )³

=(a³ -b³ -3a²b +3ab²)+(a³+b³+3a²b +3ab²)

( a - b )³ + (a + b )³ = 2 a³ + 6ab²

Now putting ,a = 2x and b = z

(2x - z)³ + (2x + z)³ =2 (2x)³ + 6 (2x) (z)²

= 2 (8x³) + 12 x z²

= 16 x³ + 12 x z²

= 4 x ( 4 x² + 3 z² )

Additional information--->

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1) (a + b)³ - (a - b)³ = 2b³ + 6a²b

2) ( a + b )² + (a - b)² = 2 ( a² + b² )

3) (a + b )² - (a - b )² = 4 a b