zadanie 32
Przedstaw każde z poniższych wyrażeń w postaci sumy algebraicznej.
a)
3(2-x)^2+4(x-5)^2=3(4-4x+x^2)+4(x^2-10x+25)=12-12x+3x^2+4x^2-40x+100=7x^2-52x+112
b)
(5x-2)(5x+2)-(3x-1)^2+4x=\cdots =25x^2-4-(9x^2-6x+1)+4x=25x^2-4-9x^2+6x-1+4x=16x^2+10x-5
c)
(3y-4)(5y+1)-(3y-4)^2+2(5y+1)^2+(y-2)(y+2)=15y^2+3y-20y-4-(9y^2-24y+16)+2(25y^2+10y+1)+y^2-4=15y^2-17y-4-9y^2+24y-16+50y^2+20y+2+y^2-4=57y^2+27y-22
d)
(x+2)^3-(x-2)(x^2+2x+4)=x^3+6x^2+12x+8-(x^3+2x^2+4x-2x^2-4x-8)=
x^3+6x^2+12x+8-x^3-2x^2-4x+2x^2+4x+8=6x^2+12x+16
e)
(2x-3)^2-4x(2x-6)+(x-5)^2=4x^2-12x+9-8x^2+24x+x^2-10x+25=-3x^2+2x+34
f)
(2x-5y)^2-4(2x+5y)^2+(5y-3)(5y+3)-(2x-5)(2x+5)=
4x^2-20xy+25y^2-4(4x^2+20xy+25y^2)+25y^2-9-(4x^2-25)=
4x^2-20xy+25y^2-16x^2-80xy-100y^2+25y^2-9-4x^2+25=
-16x^2-100xy-50y^2+16
g)
(-2a-3b)^2-(-b+2a)(-b-2a)=4a^2+12ab+9b^2-(b^2-4a^2)=4a^2+12ab+9b^2-b^2+4a^2=8a^2+12ab+8b^2
h)
(2\sqrt2+4x)(4x-2\sqrt2)-2(2x-\frac{1}{4})^2=8\sqrt2x-8+16x^2-8\sqrt2x-2(4x^2-x+\frac{1}{16})=16x^2-8-8x^2+2x-\frac{2}{16}=8x^2+2x-8\frac{1}{8}