Add the following expressions:(i) x3 -2x2y + 3xy2– y3, 2x3– 5xy2�

1.	Add the following expressions:(i) x3 -2x2y + 3xy2– y3, 2x3– 5xy2 + 3x2y – 4y3(ii) a4 – 2a3b + 3ab3 + 4a2b2 + 3b4, – 2a4 – 5ab3 + 7a3b – 6a2b2 + b4
Answer» (i) Given x³ -2x²y + 3xy²– y³, 2x³– 5xy² + 3x²y – 4y³ Collecting positive and negative like terms together, we get = x³ +2x³– 2x²y + 3x²y + 3xy² – 5xy² – y³– 4y³ = 3x³ + x²y – 2xy²– 5y³ (ii) Given a⁴ – 2a³b + 3ab³ + 4a²b²+ 3b⁴, – 2a⁴ – 5ab³ + 7a³b – 6a²b²+ b⁴ = a⁴ – 2a³b + 3ab³ + 4a²b² + 3b⁴ – 2a⁴ – 5ab³+ 7a³b – 6a²b² + b⁴ Collecting positive and negative like terms together, we get = a⁴ – 2a⁴– 2a³b + 7a³b + 3ab³ – 5ab³ + 4a²b² – 6a²b²+ 3b⁴ + b⁴ = – a⁴+ 5a³b – 2ab³ – 2a²b²+ 4b⁴

Add the following expressions:(i) x3 -2x2y + 3xy2– y3, 2x3– 5xy2 + 3x2y – 4y3(ii) a4 – 2a3b + 3ab3 + 4a2b2 + 3b4, – 2a4 – 5ab3 + 7a3b – 6a2b2 + b4

Answer»

(i) Given x³ -2x²y + 3xy²– y³, 2x³– 5xy² + 3x²y – 4y³

Collecting positive and negative like terms together, we get

= x³ +2x³– 2x²y + 3x²y + 3xy² – 5xy² – y³– 4y³

= 3x³ + x²y – 2xy²– 5y³

(ii) Given a⁴ – 2a³b + 3ab³ + 4a²b²+ 3b⁴, – 2a⁴ – 5ab³ + 7a³b – 6a²b²+ b⁴

= a⁴ – 2a³b + 3ab³ + 4a²b² + 3b⁴ – 2a⁴ – 5ab³+ 7a³b – 6a²b² + b⁴

Collecting positive and negative like terms together, we get

= a⁴ – 2a⁴– 2a³b + 7a³b + 3ab³ – 5ab³ + 4a²b² – 6a²b²+ 3b⁴ + b⁴

= – a⁴+ 5a³b – 2ab³ – 2a²b²+ 4b⁴