Question

plz answer this question​

Answer 1

Answer:

8x³ + 27y³ + 64z³ - 72xyz

Step-by-step explanation:

Given :

To find the product of :

(2x + 3y + 4z)(4x² + 9y² + 16z² - 6xy - 12yz - 8xz)

Solution :

We know that,

⇒ ( a + b + c )( a² + b² + c² - ab - bc - ac ) = a³ + b³ + c³ - 3abc

(2x + 3y + 4z)(4x² + 9y² + 16z² - 6xy - 12yz - 8xz)

⇒ (2x + 3y + 4z)( (2x)² + (3y)² + (4z)² - (2x)(3y) - (3y)(4z) - (2x)(4z) )

It is of the form,

⇒ ( a + b + c )( a² + b² + c² - ab - bc - ac )

Where a = 2x , b = 3y , c = 4z

∴ (2x + 3y + 4z)(4x² + 9y² + 16z² - 6xy - 12yz - 8xz) = (2x)³ + (3y)³ + (4z)³ - 3(2x)(3y)(4z) = 8x³ + 27y³ + 64z³ - 72xyz