Question

1/y + 4) ( 1/y + 9 ) = 1/ y^2 + ______ + 36 *​

Answer 1

Answer:

$\huge \sf \underline{ \ given\: : }$

$\bf \:( \frac{1}{y} + 4)( \frac{1}{y} + 9)$

$\huge \sf \underline{ \ identity \: used \: : }$

$\bf(x + a)(x +b )$

$\bf \to( {x})^{2} + (a + b)x + (ab)$

$\huge \sf \underline{ \ solution \: : }$

$\sf \to { \frac{1}{y} }^{2} + \frac{1}{y} (4 + 9) + (4 \times 9)$

$\sf \to { \frac{1}{y} }^{2} + \frac{1}{y} (13) + 36$

$\sf \to { (\frac{1}{y} })^{2} + \frac{13}{y} + 36$

$\sf \to {\underline { \frac{1}{y} }^{2} + { {\frac{13}{y} }}} + 36$

$\bf\therefore \: the \: number \: is \: ( \frac{13}{y} )$

$\purple{\sf \underline{ additional \:information \: : }}$

$\blue \bull\sf( {x + y})^{2} = {x}^{2} + 2xy + {y}^{2}$

$\blue \bull\sf( {x - y})^{2} = {x}^{2} - 2xy + {y}^{2}$

$\blue \bull\sf(x + y)(x - y) = {x}^{2} - {y}^{2}$

$\blue \bull \sf(x + a)(x +b ) = {x}^{2} + x(a + b ) + ab$

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