Question

1) ( 1\5 m - n ) ( 1\25 m² + 1\5mn + n² ) 2) ( 1\2 x - 1\3 y ) ( 1\4 x² + 1\6 xy + 1\9y²)

Answer 1

1) 1/125m^3+1/25m^2n+1/5mn^2-1/25m^2n-1/5mn^2-n^3
1/125m^3-n^3
2) 1/8x^3+1/12x^2y+1/18xy^2-1/12x^2y-1/18xy^2-1/27y^3
1/8x^3-1/27y^3

Answer 2

Let's simplify each of the given expressions using the distributive property of multiplication:

1. (1/5m - n) (1/25m² + 1/5mn + n²) = (1/5m)(1/25m²) + (1/5m)(1/5mn) + (1/5m)(n²) - n(1/25m²) - n(1/5mn) - n(n²) = 1/125m³ + 1/25m²n + 1/5mn² - 1/25m²n - 1/5mn² - n³ = 1/125m³ - n³

Therefore, the simplified expression is (1/125m³ - n³).

2. (1/2x - 1/3y) (1/4x² + 1/6xy + 1/9y²) = (1/2x)(1/4x²) + (1/2x)(1/6xy) + (1/2x)(1/9y²) - (1/3y)(1/4x²) - (1/3y)(1/6xy) - (1/3y)(1/9y²) = 1/8x³ + 1/12x²y + 1/18xy² - 1/12x²y - 1/18xy² - 1/27y³ = 1/8x³ - 1/27y³

Therefore, the simplified expression is (1/8x³ - 1/27y³).