Expand $(5 x - 3 y)^{3}$ .

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Solution

Expanding the given expression:
The given expression is $(5 x - 3 y)^{3}$ .
Use identity $(a - b)^{3} = a^{3} - b^{3} - 3 a b (a - b)$ to expand.
Compare expression with the identity we get, $a = 5 x, b = 3 y$ .
Substitute values in identity we have:
${(5 x - 3 y)}^{3} = {(5 x)}^{3} - {(3 y)}^{3} - 3 (5 x) (3 y) (5 x - 3 y) = 125 x^{3} - 27 y^{3} - 45 x y (5 x - 3 y) = 125 x^{3} - 27 y^{3} - 225 x^{2} y + 135 x y^{2}$
Hence, the expression, ${(5 x - 3 y)}^{3} = 125 x^{3} - 27 y^{3} - 225 x^{2} y + 135 x y^{2}$ .

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