निम्नांकित के गुणनखंड कीज�

1.	निम्नांकित के गुणनखंड कीजिए(i) \(a^2-4\)(ii) \(a^2-49b^2\)(iii) \(x^3-121x\)(iv) \(4a^2-\frac{9}{4a^2}\)(v) \(\frac{18}{x^2}-\frac{2x^2}{9}\)
Answer» (i) \(a^2-4\) = \((a)^2-(2)^2=(a+2)(a-2)\) (ii) \(a^2-49b^2\) = \((a)^2-(7b)^2=(a+7b)(a-7b)\) (iii) \(x^3-121x\) \(=x[(x)^2-(11)^2]\) \(=x(x-11)(x+11)\) (iv) \(4a^2-\frac{9}{4a^2}\) \(=(2a)^2-(\frac{3}{2a})^2\) \(=(2a+\frac{3}{2a})(2a-\frac{3}{2a})\) (v) \(\frac{18}{x^2}-\frac{2x^2}{9}\) \(=2(\frac{9}{x^2}-\frac{x^2}{9})=2[(\frac{3}{x})^2-(\frac{x}{3})^2]\) \(=2(\frac{3}{x}-\frac{x}{3})(\frac{3}{x}+\frac{x}{3})\)

निम्नांकित के गुणनखंड कीजिए(i) \(a^2-4\)(ii) \(a^2-49b^2\)(iii) \(x^3-121x\)(iv) \(4a^2-\frac{9}{4a^2}\)(v) \(\frac{18}{x^2}-\frac{2x^2}{9}\)

Answer»

(i) \(a^2-4\)

= \((a)^2-(2)^2=(a+2)(a-2)\)

(ii) \(a^2-49b^2\)

= \((a)^2-(7b)^2=(a+7b)(a-7b)\)

(iii) \(x^3-121x\)

\(=x[(x)^2-(11)^2]\)

\(=x(x-11)(x+11)\)

(iv) \(4a^2-\frac{9}{4a^2}\)

\(=(2a)^2-(\frac{3}{2a})^2\)

\(=(2a+\frac{3}{2a})(2a-\frac{3}{2a})\)

(v) \(\frac{18}{x^2}-\frac{2x^2}{9}\)

\(=2(\frac{9}{x^2}-\frac{x^2}{9})=2[(\frac{3}{x})^2-(\frac{x}{3})^2]\)

\(=2(\frac{3}{x}-\frac{x}{3})(\frac{3}{x}+\frac{x}{3})\)