Find the products:
(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) $(5 - 2 x) (3 + x)$
$= 5 (3 + x) - 2 x (3 + x)$
$= 15 + 5 x - 6 x - 2 x^{2}$
$= 15 - x - 2 x^{2}$

(ii) $(x + 7 y) (7 x - y)$
$= x (7 x - y) + 7 y (7 x - y)$
$= 7 x^{2} - x y + 49 x y - 7 y^{2}$
$= 7 x^{2} + 48 x y - 7 y^{2}$

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

(iv) $(p^{2} - q^{2}) (2 p + q)$
$= p^{2} (2 p + q) - q^{2} (2 p + q)$
$= 2 p^{3} + p^{2} q - 2 p q^{2} - q^{3}$

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Similar questions

Find the product.

(i) $(5 - 2 x) (3 + x)$ (ii) $(x + 7 y) (7 x - y)$

(iii) $(a^{2} + b) (a + b^{2})$ (iv) $(p^{2} - q^{2}) (2 p + q)$

Use the identity to find the products:

(i) (x + 6)(x − 6); (ii) (3x + 5) (3x − 5);

(iii) (2a + 4b) (2a − 4b); (iv).

(x + 4) (x + 10)

(x + 8) (x - 10)

(3 x + 4) (3 x - 5)

(y^{2} + \frac{3}{2}) (y^{2} - \frac{3}{2})

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Use the identity to compute:

(i) (x − 6)²; (ii) (3x − 5y)²; (iii) (5a − 4b)²; (iv) (p² − q²)².

(p^{2} - q^{2}) (2 p + q)

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