Use direct method to ecaluate the following products :

(i) (x + 8)(x + 3)

(ii) (y + 5)(y - 3)

(iii) (a- 8)(a+ 2)

(iv) (b - 3)(b - 5)

(v) (3x - 2y)(2x + y)

(vi) (5a + 16)(3a -7)

(vii) (8 - b)(3 + b)

Open in App

Solution

(i) $(x + 8) (x + 3) = (x \times x) + (y \times - 3) + (5 \times y) + (5 \times - 3)$

$x^{2} + 3 x + 8 x + 24$

$x^{2} + 11 x + 24$ .

(ii) $(y + 5) (y - 3) = (y \times y) + (y \times - 3) + (5 \times y) + (5 \times - 3)$

$= y^{2} + (- 3 y) + (5 y) - 15$

$= y^{2} - 3 y + 5 y - 15$

$= y^{2} + 2 y - 15$

(iii) (a - 8)(a + 2) = $(a \times a) + (a \times 2) + (- 8) \times a + (- 8) (2)$

$= a^{2} + 2 a - 8 a - 16$

$= a^{2} - 6 a - 16$ .

(iv) (b - 3)(b - 5) = $(b \times b) + (b \times - 5) + (- 3) \times b + (- 3) (- 5)$

$= b^{2} - 5 b - 3 b + 15$

$= b^{2} - 8 b + 15$

(v) (3x - 2y)(2x+ y) = $(3 x \times 2 x) + (3 x \times y) + (- 2 y \times 2 x) + (- 2 y \times y)$

$= 6 x^{2} + 3 x y - 4 x y - 2 y^{2}$

$= 6 x^{2} - x y - 2 y^{2}$

(vi) (5a + 16)(3a -7) = (5a \times 3a) + (5a \times -7) + (16 \times 3a) + 16 \times - 7\)

$= 15 a^{2} + (- 35 a) + 48 a + (- 112)$

$= 15 a^{2} - 35 a + 48 a - 112$

$= 15 a^{2} + 13 a - 112$

(vii) (8 - b)(3 + b) = $(8 \times 3) + (8 \times b) + (- b \times 3) + (- b \times b)$

$= 24 + 8 b - 3 b - b^{2}$

$= 24 + 5 b - b^{2}$

Suggest Corrections

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

Find each of the following products:
(i) $(x + 3) (x - 3)$
(ii) $(2 x + 5) (2 x - 5)$
(iii) $(8 + x) (8 - x)$
(iv) $(7 x + 11 y) (7 x - 11 y)$
(v) $(5 x^{2} + \frac{3}{4} y^{2}) (5 x^{2} - \frac{3}{4} y^{2})$
(vi) $(\frac{4 x}{5} - \frac{5 y}{3}) (\frac{4 x}{5} + \frac{5 y}{3})$
(vii) $(x + \frac{1}{x}) (x - \frac{1}{x})$
(viii) $(\frac{1}{x} + \frac{1}{y}) (\frac{1}{x} - \frac{1}{y})$
(ix) $(2 a + \frac{3}{b}) (2 a - \frac{3}{b})$