Question 67

The expression $$(a + b - c)^3 + (a - b + c)^3 - 8a^3$$is equal to:

Solution

Let $$(a + b - c) = A$$, $$(a - b + c) = B$$ and $$2a^3$$ = C

$$(a + b - c)^3 + (a - b + c)^3 - 8a^3$$

= $$(A)^3 + (B)^3 - C^3$$

$$(a^3 + b^3 + c^3 = 3abc$$ when a + b + c = 0)

So,

= -3ABC

=$$ -3(a + b - c)(a - b + c).2a^3$$

= $$6a^3(a + b - c)(c - a - b)$$

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