Find the product.
(i) $(5 - 2 x) (3 + x)$ (ii) $(x + 7 y) (7 x - y)$
(iii) $(a^{2} + b) (a + b^{2})$ (iv) $(p^{2} - q^{2}) (2 p + q)$

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Solution

(i)Given $(5 - 2 x) (3 + x) = 5 (3 + x) - 2 x (3 + x)$ =15+5x-6x-2x^2\therefore (5 − 2x)(3 + x)=-2x^2-x+15$
(ii) Given $(x + 7 y) (7 x - y) = x (7 x - y) + 7 y (7 x - y)$
$= 7 x^{2} - x y + 49 x y - 7 y^{2}$
$∴ (x + 7 y) (7 x - y) = 7 x^{2} + 48 x y - 7 y^{2}$
(iii) Given $(a^{2} + b) (a + b^{2}) = a^{2} (a + b^{2}) + b (a + b^{2})$
$∴ (a^{2} + b) (a + b^{2}) = a^{3} + a^{2} b^{2} + a b + b^{3}$
(iv) Given $(p^{2} - q^{2}) (2 p + q) = p^{2} (2 p + q) - q^{2} (2 p + q)$
$∴ (p^{2} - q^{2}) (2 p + q) = 2 p^{3} + p^{2} q - 2 p q^{2} - q^{3}$

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