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itskillerpiyush
@itskillerpiyush
October 2023
2
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please help me if this can't find on Google
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BrainlySupport
Answer:
We can simplify the given expression as follows:
$[(a + b + c)^3 - a^3] - (b^3 + c^3)$
$= [(a + b + c)^3 - a^3 - 3ab(a + b) - 3ac(a + c)] - (b^3 + c^3 - 3bc(b + c))$ (using the identity $a^3 + b^3 = (a + b)(a^2 - ab + b^2)$)
$= [3a^2b + 3a^2c + 3ab^2 + 6abc + 3ac^2 + b^3 + c^3] - [3bc^2 + 3b^2c + b^3 + c^3]$
$= 3a^2b + 3a^2c + 3ab^2 + 6abc + 3ac^2 - 3bc^2 - 3b^2c$
Therefore, the simplified expression is $3a^2b + 3a^2c + 3ab^2 + 6abc + 3ac^2 - 3bc^2 - 3b^2c$.
1 votes
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Miathegreat
Verified answer
Refer to the attachment !
:)
3 votes
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Answers & Comments
Answer:
We can simplify the given expression as follows:
$[(a + b + c)^3 - a^3] - (b^3 + c^3)$
$= [(a + b + c)^3 - a^3 - 3ab(a + b) - 3ac(a + c)] - (b^3 + c^3 - 3bc(b + c))$ (using the identity $a^3 + b^3 = (a + b)(a^2 - ab + b^2)$)
$= [3a^2b + 3a^2c + 3ab^2 + 6abc + 3ac^2 + b^3 + c^3] - [3bc^2 + 3b^2c + b^3 + c^3]$
$= 3a^2b + 3a^2c + 3ab^2 + 6abc + 3ac^2 - 3bc^2 - 3b^2c$
Therefore, the simplified expression is $3a^2b + 3a^2c + 3ab^2 + 6abc + 3ac^2 - 3bc^2 - 3b^2c$.
Verified answer
Refer to the attachment !
:)