Expand using suitable identity (0.1x – 0.2y)3

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$(0.1x – 0.2y)^3 \\ \text{Let} \: 0.1x = a, \: \: -0.2y=b \\ (a+b)^3 \\ = (a^2+2ab+b^2)(a+b) \\= a^3 + a^2b +2a^2b +2ab^2 +ab^2 +b^3 \\ = a^3 + b^3 + 2(a^2b + ab^2) +a^2b +ab^2 \\ = (0.1x)^3 +(0.2y)^3+2((0.1x)^20.2y+0.1x(0.2y)^2) +(0.1x)^20.2y + 0.1x(0.2y)^2 \\ =0.001x^3+0.008y^3+2(0.002x^2y+0.002xy^2)+0.002x^2y+0.002xy^2 \\ =0.001x^3 +0.008y^3 +0.004x^2y +0.004xy^2 +0.002x^2y +0.002xy^2 \\ =0.001x^3 +0.008y^3 +0.006x^2y+0.006xy^2 \\ =0.001 (x^3 + 8y^3 +6(x^2y+xy^2))$

Answer by Geordie Jake

Expand using suitable identity (0.1x – 0.2y)3

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