# Simplify:

(i) 2x2(x3 – x) – 3x(x4 + 2x) – 2(x4 – 3x2)

= 2x5 – 2x3 – 3x5 – 6x2 – 2x4 + 6x2

= -x5 – 2x4 – 2x3

(ii) x3y(x2 – 2x) + 2xy(x3 – x4)

= x5y – 2x4y + 2x4y – 2x5y

= -x5y

(iii) 3a2 + (a + 2) – 3a(2a + 1)
= 3a2 + a + 2 – 6a2 – 34

= -3a2 – 2a + 2

(iv) x(x + 4) + 3x(2x2 – 1) + 4x2 + 4

= x2 + 4x + 6x3 – 3x + 4x2 + 4

= 6x3 + 5x2 + x + 4

(v) a(b – c) – b(c – a) – c(a – b)

= ab – ac – bc + ab – ca + bc

= 2ab – 2ac

(vi) a(b – c) + b(c – a) + c(a – b)

= ab – ac + bc – ab + ac – bc

= 0

(vii) 4ab(a – b) – 6a2(b – b2) – 3b2(2a2 – a) + 2ab(b – a)

= 4a2b – 4ab2 – 6a2b + 6a2b2 – 6a2b2 + 3ab2 + 2ab2 – 2a2b

= 3ab2

(viii) x2(x2 + 1) – x3(x + 1) – x(x3 – x)

= x4 + x2 – x4 – x3 – x4 + x2

= 2x2 – 2x3

(ix) 2a2 + 3a (1 – 2a3) + a(a + 1)

= 2a2 + 3a – 6a4 + a2 + a

= -6a4 + 3a2 + 4a

(x) a2(2a – 1) + 3a + a3 – 8

= 2a3 – a2 + 3a + a3 – 8

= 3a3 – a2 + 3a – 8

(xii) a2b(a – b2) + ab2(4ab – 2a2) – a3b(1 – 2b)

= a3b – a2b3 + 4a2b3 – 2a3b2 – a3b + 2a3b2

= -a2b3 + 4a2b3

= 3a2b3

(xiii) a2b(a3 – a + 1) – ab(a4 – 2a2 + 2a) – b(a3 – a2 – 1)

= a5b – a3b + a2b – a5b + 2a3b – 2a2b – ba3 + a2b + b

= b

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