Question

7. Efectuați calculele știind că x, y, a,b,c aparține IR.

Answer 1

Răspuns:

$a) 5x^{2} (4xy^{2} ):(10xy) =\frac{5x^{2}(4xy^{2} ) }{10xy} =\frac{x^{2} *4xy^{2} }{2xy}=\frac{x^{2}*4y }{2}=x^{2} *2y=2x^{2} y$

$b) (14a^{2} b^{3} c):(-7ab^{2})*(-2abc )=(14a^{2} b^{3} c):(7ab^{2})*2abc =2abc*2abc=4(abc)^{2}$

$c) 2x^{4} (-\sqrt{3} x):(\sqrt{12}x^{3} )=2x^{4} (-\sqrt{3} x):(2\sqrt{3}x^{3} )=-2x^{4} \sqrt{3} x:(2\sqrt{3}x^{3} )=-x*x=-x^{2}$

$d) (-3a)(-3b)(-5a^{2} b):(-15a^{2} b^{2} )=3a*-3b*-5a^{2} b:(15a^{2} b^{2} )= \frac{3a*3b*5a^{2}b }{15a^{2} b^{2} } =\frac{a*3*5b}{5b} =3a$

$e) (-7x^{2} )(2\sqrt{2} x^{2} ):(-\sqrt{98}x^{3} )=(-7x^{2} )(2\sqrt{2} x^{2} ):(-7\sqrt{2}x^{3} )= 7x^{2} *2\sqrt{2} x^{2} :(-7\sqrt{2}x^{3} ) = \frac{7x^{2} *2\sqrt{2} x^{2}}{-7\sqrt{2}x^{3}} =\frac{x^{2}*2x^{2} }{x^{3} }= \frac{2x^{2} }{x} = 2x$

$f) (-4a^{5}) (-\frac{1}{8} a^{3} )*30a^{10} :(-5a^{15} )=-4a^{5} *-\frac{1}{8} a^{3} *30a^{10} :(-5a^{15} ) =-a^{5} *\frac{1}{2}*\frac{a^{3} *30a^{10}}{5a^{15}} =-\frac{1}{2} *\frac{a^{3} *6a^{10}}{a^{10}} =-\frac{1}{2}a^{3} *6=-a^{3}*3=-3a^{3}$