(i) 5x(2y – 3) = (5x) (2y) – (5x) (3)
= (5 × 2) (x × y) – (5 × 3) x
= 10xy – 15x
(ii) -2p (5p2 – 3p + 7)
= (-2p) (5p2) + (-2p) (-3p) + (-2p) (7)
= [(-) (+) (2 × 5) (p × p2)] + [(-) (+) (2 × 3) (p × q)] + (-) (+) (2 × 7) p
= -10p3 + 6p2 – 14p
(iii) 3mn(m3n3 – 5m2n + 7mn2)
= (3mn) (m3n3) + (3mn) (-5m2n) + (3mn)(7mn2)
= (3) (m × m3) (n × n3) + (+) (-) (3 × 5) (m × m2) (n × n) + (3 × 7) (m × m)(n × n2)
= 3m4n4 – 15m3 n2 + 21m2n3
(iv) x2 (x + y + z) + y2 (x + y + z) + z2 (x – y – z)
= (x2 × x) + (x2 × y) + (x2 × z) + (y2 × x) + (y2 × y) + (y2 × z) + (z2 × x) + z2 (-y) + z2 (-z)
= x3 + x2y + x2z + xy2 + y3 + y2z + xz2 – yz2 – z3
= x3 + y3 – z2 + x2y + x2z + xy2 + zy2 + xz2 – yz2