81x4 y4=9x22 y22=9x2+y29x2 y2 #160; #160; #160; #160; #160; #160; #160; #160; #160; #160; #160; #160; #160; #160; #160; #160; ...

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Addition and Subtraction of Algebraic Expressions

81 x4-y4

Question

81x⁴ – y⁴

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Solution

$81 x^{4} - y^{4} = {(9 x^{2})}^{2} - {(y^{2})}^{2} = (9 x^{2} + y^{2}) (9 x^{2} - y^{2}) [a^{2} - b^{2} = (a + b) (a - b)] = (9 x^{2} + y^{2}) [{(3 x)}^{2} - y^{2}] = (9 x^{2} + y^{2}) (3 x + y) (3 x - y) [a^{2} - b^{2} = (a + b) (a - b)]$

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3 x - \frac{1}{3 x} = 5

81 x^{4} + \frac{1}{81 x^{4}}

If $3 x - \frac{1}{3 x} = 5$ , find :

(i) $9 x^{2} + \frac{1}{9 x^{2}}$

(ii) $81 x^{4} + \frac{1}{81 x^{4}}$

81 x^{4} - 121 x^{2}

81 x^{4} - 16 y^{4}

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