Question

Fatore as expressões abaixo (43/44)

Answer 1

$43/44~produto~da~soma~pela~diferenca~de~dois~termos:$$quadrado~do~primeiro~termo~menos~o~quadrado~do~segundo~termo$

$43.a)\\ \\ x^{2} -49=(x+7)(x-7)$

$43.b)\\ \\ 9a^{2} -4b^{2} =(3a+2b)(3a-2b)$

$43.c)\\ \\ 1-x^{2} =(1+x)(1-x)$

$43.d)\\ \\ 4x^{2} -25y^{2} =(2x+5y)(2x-5y)$

$44.a)\\ \\ 4x^{2} -25=(2x+5)(2x-5)$

$44.b)\\ \\ x^{2} y^{2} -1=(xy+1)(xy-1)$

$44.c)\\ \\ 25x^{2} -1=(5x+1)(5x-1)$

$44.d)\\ \\ 25x^{4} -y^{6} =(5x^{2} +y^{3} )(5x^{2} -y^{3} )$

$44.e)\\ \\ \frac{1}{16} x^{2} -25=(\frac{1}{4} x+5)(\frac{1}{4} x-5)$

$44.f)\\ \\ \frac{x^{2}}{4} -\frac{1}{9} =(\frac{x}{2} +\frac{1}{3} )(\frac{x}{2} -\frac{1}{3} )$

$44.g)\\ \\ x^{2} -\frac{1}{x^{4}} =(x+\frac{1}{x^{2}} )(x-\frac{1}{x^{2}} )$

$44.h)\\ \\ \frac{9x^{2}}{4} -\frac{1}{25} =(\frac{3x}{2} +\frac{1}{5} )(\frac{3x}{2} -\frac{1}{5} )$