Question

Multiply and then evaluate:

(x² – y) and (xy – y²); when x = 1 and y = 2.

Answer 1

(x² − y) × (xy − y²)

= x² (xy − y²) − y (xy − y²)

= x³y − x²y² − xy² + y³

Verification:

When x = 1, y = 2

∴ L.H.S. = (x² − y) (xy − y²)

= [(1)² − 2] [1 × 2 − (2)²]

= (1 − 2) (2 − 4)

= − 1 × − 2

= 2

R.H.S. = x³y − x²y² − xy² + y³

= (1)³ × 2 − (1)² (2)² − 1(2)² + (2)³

= 1 × 2 − 1 × 4 − 1 × 4 + 8

= 2 − 4 − 4 + 8

= 10 − 8

= 2

∴ L.H.S. = R.H.S.