Question

Subtract: −2(xy)² (y³ + 7x²y + 5) from 5y² (x²y³ – 2x⁴y + 10x²)

Answer 1

5y² (x²y³ − 2x⁴y + 10x²) − [(−2)(xy)² (y³ + 7x²y + 5)]

= [5y²(x²y³) − 5y²(2x⁴y) + 5y²(10x²)] −[(−2)x²y²(y³ + 7x²y + 5)]

= (5y⁵x² − 10x⁴y³ + 50x²y²) − [(−2x²y²)(y³) + (−2x²y²)(7x²y) + (−2x²y²)(5)]

= 5x²y⁵ − 10x⁴y³ + 50x²y² −[−2x²y⁵ − 14x⁴y³ −10x²y²]

= 5x²y⁵ − 10x⁴y³ + 50x²y² + 2x²y⁵ + 14x⁴y³ + 10x²y²

= (5 + 2)x²y⁵ + (−10 + 14)x⁴y³ + (50 + 10)x²y²

= 7x²y⁵ + 4x⁴y³ + 60x²y²