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

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Solution

(i) $(x + 1) (x - 1) = (x)^{2} - (1)^{2}$

$= x^{2} - 1$

(ii) $(2 + a) (2 - a) = (2)^{2} - (a)^{2}$

$= 4 - a^{2}$ .

(iii) (3b - 1)(3b + 1) = $(3 b)^{2} - (1)^{2}$

$= 9 b^{2} - 1$ .

(iv) $(4 + 5 x) (4 - 5 x) = (4)^{2} - (5 x)^{2}$

$= 16 - 25 x^{2}$ .

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

$= 4 a^{2} - 9$ .

(vi) $(x y + 4) (x y - 4) = (x y)^{2} - (4)^{2}$

$= x^{2} y^{2} - 16$ .

(vii) $(a b + x^{2}) (a b - x^{2}) = (a b)^{2} - (x^{2})^{2}$

$= 9 x^{4} - 25 y^{4}$ .

(ix) $(z - \frac{2}{3}) (z + \frac{2}{3}) = (z)^{2} - {(\frac{2}{3})}^{2}$
$= z^{2} - \frac{4}{9}$ .

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

$= {(\frac{3}{5} a)}^{2} - {(\frac{1}{2})}^{2} = \frac{9}{25} a^{2} - \frac{1}{4}$ .

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

$= (0.5)^{2} - (2 a)^{2}$

$= 0.25 - 4 a^{2}$ .

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

$= \frac{a^{2}}{4} - \frac{b^{2}}{9}$ .

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