8 a - 3-27 b - 3-64 c - 3-72 abc- Factorise the polynomial

8a^3 + 27b^3 + 64c^3 72abc (2a)^3 + (3b)^3 + (4c)^3 3. 2a . 3b . 4c We know that, a^3 + b^3 + c^ 3 3abc = (a+b+c)(a^2 + b^2 + c^2 ab bc ca) (2a)^3 + ...

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Byju's Answer

Standard IX

Mathematics

Identity (x+y)(x-y)

8 a ∧ 3-27 b ...

Question

Factorise the polynomial $8 a^{3} - 27 b^{3} - 64 c^{3} - 72 a b c$

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Solution

Given polynomial $8 a^{3} + 27 b^{3} + 64 c^{3} - 72 a b c$
$= (2 a)^{3} + (3 b)^{3} + (4 c)^{3} - 3 (2 a) (3 b) (4 c)$
We know that $x^{3} + y^{3} + z^{3} - 3 x y z = (x + y + z) (x^{2} + y^{2} + z^{2} - x y - y z - z x)$
Substitute $x = 2 a, y = 3 b$ and $z = 4 c$ in the above formula, we get
$(2 a)^{3} + (3 b)^{3} + (4 c)^{3} - 3. 2 a . 3 b . 4 c = (2 a + 3 b + 4 c) [(2 a)^{2} + (3 b)^{2} + (4 c)^{2} - (2 a .3 b) - (3 b .4 c) - (4 c .2 a)]$
$= (2 a + 3 b + 4 c) (4 a^{2} + 9 b^{2} + 16 c^{2} - 6 a b - 12 b c - 8 c a)$
Therefore, the factors of the given expressions are $(2 a + 3 b + 4 c) (4 a^{2} + 9 b^{2} + 16 c^{2} - 6 a b - 12 b c - 8 c a)$

Suggest Corrections

Factorise the polynomial 8a3−27b3−64c3−72abc

Factorise the polynomial $8 a^{3} - 27 b^{3} - 64 c^{3} - 72 a b c$