Question 52

Find the product of $$(a + b + 2c)(a^{2} + b^{2} + 4c^{2} - ab - 2bc - 2ca)$$

Solution

$$(a + b + 2c)(a^{2} + b^{2} + 4c^{2} - ab - 2bc - 2ca)$$

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

$$(\because a^3 + b^3 + c^3 - 3abc = (a + b + c)(a^{2} + b^{2} + c^{2} - ab - bc - ca))$$

$$= a^3 + b^3 + 8c^3 - 6abc$$

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