(a) What should be added to x³ + 3x²y + 3xy² + y³ to get x³ + y³?

(b) What should be added to 3pq + 5p²q² + p³ to get p³ + 2p²q² + 4pq?

Add the following expressions:

(a) p² – 7pq – q² and – 3p² – 2pq + 7q²

(b) x³–x²y–xy² –y³ and x³ –2x²y+3xy²+4y

(c) ab + bc + ca and – bc – ca – ab

(d) p² – q + r, q² – r + p and r² – p + q

(e) x³y² + x²y³ +3y⁴ and x⁴ + 3x²y³ + 4y⁴

(f) p²qr + pq²r + pqr² and – 3pq²r –2pqr²

(g) uv – vw, vw – wu and wu – uv

(h) a² + 3ab – bc, b² + 3bc – ca and c² + 3ca – ab

(i) p⁴ + 2p² + -17p + p² and

(j) t – t² – t³ – 14; 15t³ + 13 + 9t – 8t²; 12t² – 19 – 24t and 4t – 9t² + 19t³

Subtract

(a) –7p²qr from – 3p²qr.

(b) –a² – ab from b² + ab.

(c) –4x²y – y³ from x³ + 3xy² – x²y.

(d) x⁴ + 3x³y³ + 5y⁴ from 2x⁴ – x³y³ + 7y⁴.

(e) ab – bc – ca from – ab + bc + ca.

(f) –2a² – 2b² from – a² – b² + 2ab.

(g) x³y² + 3x²y² – 7xy³ from x⁴ + y⁴ + 3x²y² – xy³.

(h) 2(ab + bc + ca) from –ab – bc – ca.

(i) 4.5x⁵ –3.4x²+5.7 from 5x⁴–3.2x²–7.3x.

(j) 11 – 15y² from y³ – 15y² – y – 11.

(a) What should be subtracted from 2x³ – 3x²y + 2xy² + 3y³ to get x³ – 2x²y + 3xy² + 4y³?

(b) What should be subtracted from –7mn + 2m² + 3n² to get m² + 2mn + n²?

How much is 21a³ – 17a² less than 89a³ – 64a² + 6a + 16?