Expand $(7 x - 9 y)^{3}$ [3 marks]

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Solution

Let us simplify the expression, we get
$(7 x - 9 y)^{3} = (7 x)^{3} - [3 \times (7 x)^{2} \times 9 y] + [3 \times (7 x) \times (9 y)^{2}] - (9 y)^{3}$
By using the formula,
$(a - b)^{3} = a^{3} - 3 a^{2} b + 3 a b^{2} - b^{3}$
(1 mark)
Here $a = 7 x, b = - 9 y$
Now, substituting the above values, we get
$= 343 x^{3} - [3 \times 49 x^{2} \times 9 y] + [3 \times 7 x \times 81 y^{2}] - 729 y^{3}$
$= 343 x^{3} - 1323 x^{2} y + 1701 x y^{2} - 729 y^{3}$
$∴ (7 x - 9 y)^{3} = 343 x^{3} - 1323 x^{2} y + 1701 x y^{2} - 729 y^{3}$
(2 marks)

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