Find each of the following products- i x-3x-3 ii 2x-52x-5 iii 8-x8-x iv 7x-11y7x-11y v 5x2-3-4y2 5x2-3-4y2 vi 4x-5-5y-3 4x-5-5y-3 vii x-1-x x-1-x viii 1-x-1-y 1-x-1-y ix 2a-3-b 2a-3-b

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Multiplication of Any Polynomial

Find each of ...

Question

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

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Solution

(i) $(x + 3) (x - 3) = (x)^{2} - (3)^{2} = x^{2} - 9$

(ii) $(2 x + 5) (2 x - 5) = (2 x)^{2} - (5)^{2} = 4 x^{2} - 25$

(iii) $(8 + x) (8 - x) = (8)^{2} - (x)^{2} = 64 - x^{2}$

(iv) $(7 x + 11 y) (7 x - 11 y) = (7 x)^{2} - (11 y)^{2} = 49 x^{2} - 121 y^{2}$

(v) $(5 x^{2} + \frac{3}{4} y^{2}) (5 x^{2} - \frac{3}{4} y^{2}) = (5 x^{2})^{2} - {(\frac{3}{4} y^{2})}^{2} = 25 x^{4} - \frac{9}{16} y^{4}$

(vi) $(\frac{4 x}{5} - \frac{5 y}{3}) (\frac{4 x}{5} + \frac{5 y}{3}) = {(\frac{4 x}{5})}^{2} - {(\frac{5}{3} y)}^{2} = \frac{16}{25} x^{2} - \frac{25}{9} y^{2}$

(vii) $(x + \frac{1}{x}) (x - \frac{1}{x}) = (x)^{2} - {(\frac{2}{x})}^{2} = x^{2} - \frac{1}{x^{2}}$

(viii) $(\frac{1}{x} + \frac{1}{y}) (\frac{1}{x} - \frac{1}{y}) = {(\frac{1}{x})}^{2} - {(\frac{1}{y})}^{2} = \frac{1}{x^{2}} - \frac{1}{y^{2}}$

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

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Similar questions

Q. Find each of the following products:
(i) (x + 3)(x − 3)
(ii) (2x + 5)(2x − 5)
(iii) (8 + x)(8 − x)
(iv) (7x + 11y)(7x − 11y)
(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})

Solve the equations:

(i) 5x = 3x + 24;

(ii) 8t + 5 = 2t − 31;

(iii) 7x − 10 = 4x + 11;

(iv) 4z + 3 = 6 + 2z;

(v) 2x − 1 = 14 − x;

(vi) 6x + 1 = 3(x − 1) + 7;

(vii) ;

(viii) ;

(ix) 3(x + 1) = 12 + 4 (x − 1);

(x) 2x − 5 = 3(x − 5);

(xi) 6(1 − 4x) + 7(2 + 5x) = 53;

(xii) 3(x + 6) + 2 (x + 3) = 64;

(xiii) ;

(xiv) .

Q. Solve the following equations.

(i)

\frac{x^{2} + 12 x - 20}{3 x - 5} = \frac{x^{2} + 8 x + 12}{2 x + 3}

(ii)

\frac{10 x^{2} + 15 x + 63}{5 x^{2} - 25 x + 12} = \frac{2 x + 3}{x - 5}

(iii)

\frac{{(2 x + 1)}^{2} + {(2 x - 1)}^{2}}{{(2 x + 1)}^{2} - {(2 x - 1)}^{2}} = \frac{17}{8}

(iv)

\frac{\sqrt{4 x + 1} + \sqrt{x + 3}}{\sqrt{4 x + 1} - \sqrt{x + 3}} = \frac{4}{1}

(v)

\frac{{(4 x + 1)}^{2} + {(2 x + 3)}^{2}}{4 x^{2} + 12 x + 9} = \frac{61}{36}

(vi)

\frac{{(3 x - 4)}^{3} - {(x + 1)}^{3}}{{(3 x - 4)}^{3} + {(x + 1)}^{3}} = \frac{61}{189}

Q. Use the identity

(x + a) (x + b) = x^{2} + (a + b) x + a b

to find following products.
(i)

(x + 3) (x + 7)

(ii)

(4 x + 5) (4 x + 1)

(iii)

(4 x - 5) (4 x - 1)

(iv)

(4 x + 5) (4 x - 1)

(v)

(2 x + 5 y) (2 x + 3 y)

(vi)

(2 a^{2} + 9) (2 a^{2} + 5)

(vii)

(x y z - 4) (x y z - 2)

Solve :

$(i) \frac{1}{3} x - 6 = \frac{5}{2} (i i) \frac{2 x}{3} - \frac{3 x}{8} = \frac{7}{12} (i i i) (x + 2) (x + 3) + (x - 3) (x - 2) - 2 x (x + 1) = 0 (i v) \frac{1}{10} - \frac{7}{x} = 35 (v) 13 (x - 4) - 3 (x - 9) - 4 (x + 4) = 0 (v i) x + 7 - \frac{8 x}{3} = \frac{17 x}{6} - \frac{5 x}{8} (v i i) \frac{3 x - 2}{4} - \frac{2 x + 3}{3} = \frac{2}{3} - x (v i i i) \frac{x + 2}{6} - (\frac{11 - x}{3} - \frac{1}{4}) = \frac{3 x - 4}{12} (i x) \frac{2}{5 x} - \frac{5}{3 x} = \frac{1}{15} (x) \frac{x + 2}{3} - \frac{x + 1}{5} = \frac{x - 3}{4} - 1 (x i) \frac{3 x - 2}{3} + \frac{2 x + 3}{2} = x + \frac{7}{6} (x i i) x - \frac{x - 1}{2} = 1 - \frac{x - 2}{3} (x i i i) \frac{9 x + 7}{2} - (x - \frac{x - 2}{7}) = 36 (x i v) \frac{6 x + 1}{2} + 1 = \frac{7 x - 3}{3}$

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Find each of the following products: (i) (x+3)(x−3) (ii) (2x+5)(2x−5) (iii) (8+x)(8−x) (iv) (7x+11y)(7x−11y) (v) (5x2+34y2)(5x2−34y2) (vi) (4x5−5y3)(4x5+5y3) (vii) (x+1x)(x−1x) (viii) (1x+1y)(1x−1y) (ix) (2a+3b)(2a−3b)