Question

Factorize each of the following expressions:
2√2a³+16√2b³+c³-12abc

Answer 1

Answer:

is in the given fig.

(√2a+2√2b+c)(√2a^2+8b^2+c-4ab-2√2bc-√2ac)

Step-by-step explanation:

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Answer 2

The algebraic expression is given as : 2√2a³ + 16√2b³ + c³ - 12abc

 

We can rewrite the  given expression as :  

(√2a)³ + (2√2b)³ + (c)³ − 3(√2a)(2√2b)(c)

We know, a³ + b³ + c³ − 3abc = (a + b + c)(a² + b² + c²− ab − bc − ca)

= (√2a +  2√2b + c){ (√2a)² + (2√2b)² + (c)²  −√2a × 2√2b − (2√2b) × (c) − © ×√2a}

= (√2a  +  2√2b + c ) {2a² + 8b² + c² - 4ab -  2√2bc - √2ca}

Hence  the factors of 2√2a³ + 16√2b³ + c³ - 12abc is (√2a  +  2√2b + c ) {2a² + 8b² + c² - 4ab -  2√2bc  - √2ca}.

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