Question

factorise:

a4+b4+c4-2b2c2-2a2c2-2a2b2​

Answer 1

Answer:

This is the step by step explanation (in picture)

Answer 2

The factor form of given expression is (a - b - c) (a + b - c) (a - b + c) (a + b + c).

Step-by-step explanation:

The given expression is

$a^4+b^4+c^4-2b^2c^2-2a^2c^2-2a^2b^2$

It can be rewritten as

$(a^2)^2+(b^2)^2+(c^2)^2-2b^2c^2-2a^2c^2-2a^2b^2+2a^2c^2-2a^2c^2$

$[(a^2)^2+(b^2)^2+(c^2)^2-2b^2c^2+2a^2c^2-2a^2b^2]-2a^2c^2-2a^2c^2$

Using the properties of algebra we get

$(a^2-b^2+c^2)^2-4c^2a^2$        $[\because (a-b+c)^2=a^2+b^2+c^2-2ab+2ac-2bc]$

$(a^2-b^2+c^2)^2-(2ca)^2$

$(a^2-b^2+c^2-2ca)(a^2-b^2+c^2+2ca)$       $[\because a^2-b^2=(a+b)(a-b)]$

$[(a-c)^2-b^2][(a+c)^2-b^2]$

$[(a-c-b)(a-c+b)][(a+c-b)(a+c+b)]$          $[\because a^2-b^2=(a+b)(a-b)]$

$(a - b - c) (a + b - c) (a - b + c) (a + b + c)$

Therefore, the factor form of given expression is (a - b - c) (a + b - c) (a - b + c) (a + b + c).

#Learn more

How to Factorise a4-b4.

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