(i) (7x – 8) (3x + 2) = 7x(3x + 2) – 8 (3x + 2)
= 21x^{2} + 14x – 24x – 16 = 21x^{2} – 10x – 16
(ii) (px –q) (px + q) = px(px + q) – q(px + q)
= p^{2}x^{2} + pxq – pqx – q^{2} = p^{2}x^{2 }– q^{2}
(iii) (5a + 5b – c) (2b – 3c)
= 5a (2b – 3c) + 5b(2b – 3c) – c(2b – 3c)
= 10ab – 15ac + 10b^{2} – 15bc – 2bc + 3c^{2}
= 10ab + 10b^{2 }– 17bc – 15ac + 3c^{2}
(iv) (4x – 5y) (5x – 4y)
= 4x(5x – 4y) – 5y (5x – 4y)
= 20x^{2 }– 16xy – 25xy + 20y^{2}
= 20x^{2} – 41xy + 20y^{2}
(v) (3y + 4z) (3y – 4z) + (2y + 7z) (y + z)
= 3y (3y – 4z) + 4z(3y – 4z) + 2y(y + z) + 7z(y + z)
= 9y^{2 }– 12yz + 12yz – 16z^{2 }+ 2y^{2} + 2yz + 7yz + 7z^{2}
= (9 + 2)y^{2} + (-12 + 12 + 2 + 7) yz + (-16 + 7)z^{2}
= 11y^{2} +9yz – 9z^{2}