(i) 8ab^{2} × -4a^{3}b^{4} = (8 × -4) (ab^{2 }× a^{3}b^{4})

= -32a ^{1+3}, b^{2+4}

= - 32a^{4}b^{6}

(ii) (2/3) ab × (-(1/4)a^{2}b ) = (2/3 × (-1/4) (ab × a^{2}b)

= - (1/6)a^{1+2 }. b ^{1+ 1}

= -(1/6)a^{3}b^{2}

(iii) -5cd^{2 }× (-5cd^{2 })= (-5 × -5) (cd^{2} × cd^{2})

= 25c^{1+1 }d^{2+2}

= 25c^{2}d^{4}

(iv) 4a (6a + 7)

= 4a × 6a + 4a × 7

= 24a^{2} + 28a

(v) -8x (4 – 2x – x^{2})

= -8x × 4 – 8x × (-2x) – 8x × (-x^{2})

= -32x + 16x^{2} + 8x^{3}

(vi) -3a (2a^{2} – 5a – 4)

= -3a × 2a^{2} – 5a × (-3a) – 4 × (-3a)

= -6a^{3} + 15a^{2} + 12a

(vii) (x + 4) (x -5) = x (x -5) + 4 (x – 5)

= x^{2} – 5x + 4x – 20

= x^{2} – x – 20

(viii) (5a – 1) (7a – 3)

= 5a (7a – 3) – 1(7a – 3)

= 35a^{2} – 15a – 7a + 3

= 35a^{2} – 22a + 3

(ix) (12a + 5b) (7a – b) = 12a (7a – b) + 5b (7a – b)

= 84a^{2} – 12ab + 35ab – 5b^{2}

= 84a^{2} + 23ab – 5b^{2}

(x) (x^{2} + x +1) (1 – x) = 1 (x^{2} + x + 1) – x(x^{2 }+ x + 1)

= x^{2 }+ x + 1 – x^{3} – x^{2 }– x

= 1- x^{3}

(xi) (2m^{2 }– 3m – 1) (4m^{2} – m – 1)

= 2m^{2} (4m^{2} – m – 1) – 3m(4m^{2 }– m – 1) – 1(4m^{2} – m – 1)

= 8m^{4 }- 2m^{3} – 2m^{2} – 12m^{3 }+3m^{2 }+ 3m - 4m^{2} + m + 1

= 8m^{4} – 14m^{3} – 6m^{2 }+ 3m^{2 }+ 4m + 1

= 8m^{4} – 14m^{3} – 3m^{2 }+ 4m + 1

(xii) a^{2} × ab × b^{2}

= a^{2+1 }. b^{1+2}

= a^{3}b^{3}

(xiii) abx × (-3a^{2}x) × 7b^{2}x^{3}

= (-3 × 7) (a × a^{2}) (b × b^{2}) (x × x × x^{3})

= -21a^{3}b^{3}x^{5}

(xiv) -3bx × (-5xy) × (-7b^{3}y^{2})

= (-3 × -5 × -7) (b × b^{3}) (x × x) (y × y^{2})

= -105 b^{4} x^{2}y^{3}

(xv) ( -(3/2)x^{5}y^{3} ) ((4/9)a^{2}x^{3}y)

= ( -(3/2) × 4/9) (a^{2})(x^{5} × x^{3})(y^{3 }× y)

= (-2/3) a^{2}x^{8}y^{4}

(xvi) (-(2/3)a^{7 }b^{2}) (-(9/4)ab^{5})

= (-(2/3) × (-9/4)) (a^{7} × a) (b^{2} × b^{5})

= 3/2 a^{8}b^{7}

(xvii) (2a^{3} – 3a^{2}b) (-(1/2)ab^{2})

= -(1/2)ab^{2} (2a^{3} – 3a^{2}b)

= 2a^{3} × -(½)ab^{2} – 3a^{2}b × -(½) ab^{2}

= - a^{4}b^{2} + (3/2)a^{3}b^{3}

(xviii) (2x + (½)y ) (2x – ( ½)y)

= 2x (2x – (½)y) + (½)y (2x – (½)y)

= 4x^{2} – xy + xy – (¼)y^{2}

= 4x^{2 }– (¼)y^{2}