Zadanie 1
a)
x^3-36x^2-4x-144=
=x^2(x-36)-4(x-36)= …(x-36) wyłączam przed nawias
=(x-36)(x^2-4)=
=(x-36)(x-2)(x+2)
b)
(e+f)^2-49e^2=
(e+f)^2-(7e)^2=
=(e+f-7e)(e+f+7e)=
=(f-6e)(8e+f)
c)
1+x-8x^2+8x^3=
=(1+x)-8x^2(1-x)=
=(1-x)(1-8x^2)=
=(1-x)[1-(\sqrt8x)^2]= …\sqrt{8}=\sqrt{4*2}=2\sqrt2
=(1-x)(1-2\sqrt2x)(1+2\sqrt2x)
d)
(a^4b^4-16)(a^2b^2-49)=
=[(a^2b^2)^2-4^2][(ab)^2-7^2]=
=(a^2b^2-4)(a^2b^2+4)(ab-7)(ab+7)=
=(ab-2)(ab+2)(a^2b^2+4)(ab-7)(ab+7)
wzór skróconego mnożenia
a^2-b^2=(a-b)(a+b)