"a+2c+3b=0 then what is a3+8b3+27c3?" was answered by our experts

High School
Algebra
Pre-Algebra
Equations, expressions, and inequalitie

felpillauvc

Answered question

2022-02-05

a + 2 c + 3 b = 0

then what is

a^{3} + 8 b^{3} + 27 c^{3}

Answer & Explanation

ungabav6k

Beginner2022-02-06Added 8 answers

We can rewrite one of the letters as an expression in the others.
$a + 2 c + 3 b = 0 \to a = - 2 c - 3 b$
Then we replace every a in the second expression:
$a^{3} + 8 b^{3} + 27 c^{3} =$
${(- 2 c - 3 b)}^{3} + 8 b^{3} + 27 c^{3} =$
$(- 8 c^{3} - 36 b c^{2} - 54 b^{2} c - 19 b^{3}) + 8 b^{3} + 27 c^{3} =$
$19 c^{3} - 36 b c^{2} - 54 b^{2} c - 10 b^{3}$
Then the $b^{3} s and c^{3} s$ would have cancelled out nicer.
$a = - 2 b - 3 c$
${(- 2 b - 3 c)}^{3} + 8 b^{3} + 27 c^{3} =$
$(- 8 b^{3} - 36 b^{2} c - 54 c^{2} - 27 c^{3}) + 8 b^{3} + 27 c^{3} =$
$- 36 b^{2} c - 54 b c^{2} or 18 b c (- 2 b - 3 c)$
and, since $a = - 2 b - 3 c$ we can rewrite that:
Answer:
$a^{3} + 8 b^{3} + 27 c^{3} = 18 a b c$

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