The correct option is A 64x^3 144x^2y + 108 xy^2 27y^3 We know, (a b)^3=a^3 b^3 3ab(a b) #160; (a b)^3=a^3 b^3 3a^2b+3ab^2 .Then, ...

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Equations

Expand 4x -...

Question

Expand $(4 x - 3 y)^{3}$ .

64 x^{3} - 144 x^{2} y + 108 x y^{2} - 27 y^{3}

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64 x^{3} + 144 x^{2} y + 108 x y^{2} - 27 y^{3}

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64 x^{3} - 144 x^{2} y - 108 x y^{2} - 27 y^{3}

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None of these

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Solution

The correct option is A $64 x^{3} - 144 x^{2} y + 108 x y^{2} - 27 y^{3}$
We know, $(a - b)^{3} = a^{3} - b^{3} - 3 a b (a - b)$
$⟹$ $(a - b)^{3} = a^{3} - b^{3} - 3 a^{2} b + 3 a b^{2}$ .

Then,
$(4 x - 3 y)^{3}$
$= (4 x)^{3} - (3 y)^{3}$ $- 3 (4 x)^{2} (3 y)$ $+ 3 (4 x) (3 y)^{2}$
$= 64 x^{3} - 144 x^{2} y + 108 x y^{2} - 27 y^{3}$ .

Therefore, option $A$ is correct.

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