Evaluate :

(i) $(3 x + \frac{1}{2}) (2 x + \frac{1}{3})$

(ii) $(2 a + 0.5) (7 a - 0.3)$

(iii) $(9 - y) (7 + y)$

(iv) $(2 - z) (15 - z)$

(v) $(a^{2} + 5) (a^{2} - 3)$

(vi) $(4 - a b) (8 + a b)$

(vii) $(5 x y - 7) (7 x y + 9)$

(viii) $(3 a^{2} - 4 b^{2}) (8 a^{2} - 3 b^{2})$

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Solution

(i) $(3 x + \frac{1}{2}) (2 x + \frac{1}{3}) = 3 x (2 x + \frac{1}{3}) + \frac{1}{2} (2 x + \frac{1}{3}) = 6 x^{2} + x + x + \frac{1}{6} = 6 x^{2} + 2 x + \frac{1}{6}$

(ii) $(2 a + 0.5) (7 a - 0.3) = 2 a (7 a - 0.3) + 0.5 (7 a - 0.3) = 14 a^{2} - 0.6 a + 3.5 a - 0.15 = 14 a^{2} + 2.9 a - 0.15$

(iii) $(9 - y) (7 + y) = 9 (7 + y) - y (7 + y) = 63 + 9 y - 7 y - y^{2} = 63 + 2 y - y^{2}$

(iv) $(2 - z) (15 - z) = 2 (15 - z) - z (15 - z) = 30 - 2 z - 15 z + z^{2} = 30 - 17 z + z^{2}$

(v) $(a^{2} + 5) (a^{2} - 3) = a^{2} (a^{2} - 3) + 5 (a^{2} - 3) = a^{4} - 3 a^{2} + 5 a^{2} - 15 = a^{4} + 2 a^{2} - 15$

(vi) $(4 - a b) (8 + a b) = 4 (8 + a b) - a b (8 + a b) = 32 + 4 a b - 8 a b - a^{2} b^{2} = 32 - 4 a b - a^{2} b^{2}$

(vii) $(5 x y - 7) (7 x y + 9) = 5 x y (7 x y + 9) - 7 (7 x y + 9) = 35 x^{2} y^{2} + 45 x y - 49 x y - 63 = 35 x^{2} y^{2} - 4 x y - 63$

(viii) $(3 a^{2} - 4 b^{3}) (8 a^{2} - 3 b^{2}) = 3 a^{2} (8 a^{2} - 3 b^{2}) - 4 b^{2} (8 a^{2} - 3 b^{2}) = 24 a^{4} - 9 a^{2} b^{2} - 32 a^{2} b^{2} + 12 b^{4} = 24 a^{4} - 41 a^{2} b^{2} + 12 b^{4}$

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Similar questions

Use direct method to evaluate :

(i) (x + 1)(x - 1)

(ii) (2 + a)(2 - a)

(iii) (3b - 1)(3b + 1)

(iv) ( 4 + 5x)(4 - 5x)

(v) (2a + 3)(2a - 3)

(vi) (xy + 4)(xy - 4)

(vii) (ab + x^2)(ab - x^2)

(viii) (3x^2 + 5y^2)(3x^2 - 5y^2)

(vi) (xy + 4)(xy - 4)

(ix) $(z - \frac{2}{3}) (z + \frac{2}{3})$

(x) $(\frac{3}{5} a + \frac{1}{2}) (\frac{3}{5} a - \frac{1}{2})$

(xi) (0.5 - 2a)(0.5 + 2a)

(xii) $(\frac{a}{2} - \frac{b}{2}) (\frac{a}{2} + \frac{b}{3})$

(3 a^{2} - 4 b^{2}) (8 a^{2} - 3 b^{2})

24 a^{4} - 41 a^{2} b^{2} + 12 b^{4}

If 2a + 3b = 8 then express $3 b^{2} - 2 b + 3$ in terms of a.

12 a b - 10 b^{2} - 18 a^{2}

9 a b + 12 b^{2} + 14 a^{2}

a b + 2 b^{2}

3 b^{2} - a^{2} .

Evaluate :

(i) $(2 x - \frac{3}{5}) (2 x + \frac{3}{5})$

(ii) $(\frac{4}{7} a + \frac{3}{4} b) (\frac{4}{7} a - \frac{3}{4} b)$

(iii) $(6 - 5 x y) (6 + 5 x y)$

(iv) $(2 a + \frac{1}{2 a}) (2 a - \frac{1}{2 a})$

(v) $(4 x^{2} - 5 y^{2}) (4 x^{2} + 5 y^{2})$

(vi) $(1.6 x + 0.7 y) (1.6 x - 0.7 y)$

(vii) $(m + 3) (m - 3) (m^{2} + 9)$

(viii) $(3 x + 4 y) (3 x - 4 y) (9 x^{2} + 16 y^{2})$

(ix) $(a + b c) (a - b c) (a^{2} + b^{2} c^{2})$

(x) $203 \times 197$

(xi) $20.8 \times 19.2$

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