Let us simplify the expression, we get (7x 9y)^3=(7x)^3 [3× (7x)^2×9y]+[3× (7x)× (9y)^2] (9y)^3 By using the formula, (a b)^3=a^3 3a^2b+3ab^2 b^3 Here a=7x,b= 9 ...

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Standard IX

Mathematics

Algebraic Identity 1

Expand 7x-9y3

Question

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

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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,
$(a - b)^{3} = a^{3} - 3 a^{2} b + 3 a b^{2} - b^{3}$
Here $a = 7 x, b = - 9 y$
Now, substituting the above values, we get
$= 343 x^{3} - [3 \times 49 x^{2} \times 9 y] + [3 \times 7 x \times 81 y^{2}] - 729 y^{3}$
$= 343 x^{3} - 1323 x^{2} y + 1701 x y^{2} - 729 y^{3}$
$∴ (7 x - 9 y)^{3} = 343 x^{3} - 1323 x^{2} y + 1701 x y^{2} - 729 y^{3}$

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Expand (7x−9y)3

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