Factorize- 2 -2 a3-16 -2 b3-c3-12 abc

2√2a3+16√2b3+c3 12abc = √8a3+√512b3+c3 12abc Now √8a3= (√2a)3 √512b3= (√8b)3 and 3(√2a)(√8b)c = 3√16 abc= 3(4)abc = 12abc Hence the expression follows the pa ...

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Standard IX

Mathematics

Polynomials

factorize: 2 ...

Question

factorize: 2√2a³+16√2b³+c³-12abc

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Solution

2√2a³+16√2b³+c³-12abc
= √8a³+√512b³+c³-12abc
Now √8a³= (√2a)³√512b³= (√8b)^{3
and 3(}√2a)(√8b)c = 3√16 abc= 3(4)abc = 12abc
Hence the expression follows the pattern x³+y³+z³-3xyz
with x = √2a, y=√8b and z= c
Factors are (x+y+z)(x²+y²+z²-xy-yz-zx)
=( √2a+√8b +c)(2a²+8b²+c²-√16ab-√8bc-√2ac) using √16=4 and √8=2√2 we get
= ( √2a+2√2b +c)(2a²+8b²+c²-4ab-2√2bc-√2ac) Answer

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factorize: 2√2a3+16√2b3+c3-12abc

factorize: 2√2a³+16√2b³+c³-12abc