Question

Проффессоры и Ученые помоги пожалуйста с Домашним заданием!

Answer 1

$2) frac{ 7^{6} * 2^{6} }{ 14^{5} } * 28^{-1} + frac{ 2^{3} }{16} = frac{ 14^{6} }{ 14^{5} } * frac{1}{2*14} + frac{8}{16} = frac{14}{2*14} + frac{1}{2} =1$

$4) frac{ 23^{2} - 13^{2} }{4* 3^{2} } = frac{10*4* 3^{2} }{4* 3^{2} } =10$

$6) frac{ 96^{2} - 54^{2} }{ 83^{2} - 67^{2} } = frac{(96-54)(96+54)}{(83-67)(83+67)} = frac{42*150}{16*150} = frac{21}{8} =2,625$

$8) 112^{2} -2*112*56+ 56^{2} = (112-56)^{2} = 56^{2} =3136$


$2)9 x^{2} -16 y^{2} =(3x-4y)(3x+4y)$

$4) x^{3} - (2y)^{3} =(x-2y)( x^{2} +2xy+ y^{2} )$

$6)8 x^{3} -125 y^{3} =(2x-5y)(4 x^{2} +10xy+25 y^{2} )$

$8) x^{2} - b^{2} -ax-ab=(x-b)(x+b)-a(x+b)=(x+b)(x-b-a)$

$10) a^{2} x^{2} - y^{4} = (ax)^{2} - y^{4} =(ax- y^{2} )(ax+ y^{2} )$

$12) c^{2} -4c+4-9 x^{2} = (c-2)^{2} - (3x)^{2} =(c-2-3x)(c-2+3x)$

$16)3 x^{2} +2x-xy-2 y^{2} + y^{3} -3x y^{2} =[tex](x- y^{2} )(3x+2-y)$)[/tex]

$14)4 c^{2} +20c+25-9 a^{2} =(4 c^{2} +10c)+(10c+25)-9 a^{2} =$
$4c(c+2,5)+10(c+2,5)-9 a^{2} = (2c+5)^{2} - (3a)^{2} =$
$(2c+5-3a)(2c+5+3a)$

$18) a^{2} x+a+a x^{2} +x+2ax+2=ax(a+x)+(a+x)+2(ax+1)=$
$(a+x)(ax+1)+2(ax+1)=(ax+1)(a+x+2)$