Multiply :

(i) $2 x^{2} - 4 x + 5 b y x^{2} + 3 x - 7$

(ii) $(a b - 1) (3 - 2 a b)$

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Solution

(i) $2 x^{2} - 4 x + 5 b y x^{2} + 3 x - 7 2 x^{2} - 4 x + 5 b y x^{2} + 3 x - 7 (2 x^{2} - 4 x + 5) \times (x^{2} + 3 x - 7) 2 x^{2} (x^{2} + 3 x - 7) - 4 x (x^{2} + 3 x - 7) + 5 (x^{2} + 3 x - 7) 2 x^{4} + 6 x^{3} - 14 x^{2} - 4 x^{3} - 12 x^{2} + 28 x + 5 x^{2} + 15 x - 35 2 x^{4} + 6 x^{3} - 4 x^{3} - 14 x^{2} - 12 x^{2} + 5 x^{2} + 28 x + 15 x - 35 2 x^{4} + 2 x^{3} - 21 x^{2} + 43 x - 35 (i i) (a b - 1) (3 - 2 a b) a b (3 - 2 a b) - 1 (3 - 2 a b) 3 a b - 2 a^{2} b^{2} - 3 + 2 a b - 2 a^{2} b^{2} + 5 a b - 3 2 a^{2} b^{2} - 5 a b + 3$

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Identify polynomials in the following :

(i) f(x) = $4 x^{3} - x^{2}$ - 3x + 7

(ii) g(x) = $2 x^{3} - 3 x^{2} + \sqrt{x} - 1$

(iii) p(x) = $\frac{2}{7} x^{2} - \frac{7}{4} x + 9$

(iv) q(x) = $2 x^{2} - 3 x + \frac{4}{x} + 2$

(v) h(x) = $x^{4} - x^{\frac{3}{2}} + x - 1$

(vi) f(x) = 2 + $\frac{3}{x} + 4 x$

8 a - 6 a b + 5 b, - 6 a - a b - 8 b and - 4 a + 2 a b + 3 b

5 x^{3} + 7 + 6 x - 5 x^{2}, 2 x^{2} - 8 - 9 x, 4 x - 2 x^{2} + 3 x^{3}, 3 x^{3} - 9 x - x^{2} and x - x^{2} - x^{3} - 4

x^{2} + 4 x - 5

2 x^{2} - 3 x + 1

\frac{3 x + 5}{x^{2} + 4 x + 13}

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