Question

Zredukuj do najprostrzej postaci

a) 2x(x-5)+3(x²-2)+(x+4)²-2(x-2)(x+2)=

b) 4(3-x²)+4(x-1)²-3x(2-x)+(3-x)(3+x)=

c) (x-5)²-3(x-1)-(x+1)-(2x²-1)+x(2x-3)=

d)(4+x)(4-x)-2x(1-3x)+2(x+2)²-4(x²-1)=

Answer 1

A) 2x²-10x+3x²-6+x²+16-2x²+8x-8=4x²-2x+2
b) 12-4x²+4x²-4-6x+3x²+9-6x+x²=17+4x²-12x
c) x²-25-3x+3-x-1-2x²+1+2x²-3x=x²-22-7x
d) 16-8x+x²-2x+6x²+2x²+8-4x²+4=28-8x+5x²

Answer 2

A) 2x(x-5)+3(x²-2)+(x+4)²-2(x-2)(x+2)=
2x²-10x+3x²-6+x²+8x+16-2(x²-4)=
6x²-2x+10-2x²+8=
4x²-2x+18=
2x(2x-1)+18

b) 4(3-x²)+4(x-1)²-3x(2-x)+(3-x)(3+x)=
12-4x²+4(x²-2x+1)-6x+3x²+(9-x²)=
12-4x²+4x²-8x+4-6x+3x²+9-x²=
12-14x+2x²+13=
2x²-14x+25=
2x(x-7)+25

c) (x-5)²-3(x-1)-(x+1)-(2x²-1)+x(2x-3)=
x²-10x+25-3x+3-x-1-2x²+1+2x²-3x=
x²-17x+28=
x(x-17)+28

d)(4+x)(4-x)-2x(1-3x)+2(x+2)²-4(x²-1)=
16-x²-2x+6x²+2(x²+4x+4)-4x²+4=
16-x²-2x+6x²+2x²+8x+8-4x²+4=
3x²+6x+28=
3x(x+2)+28

Answer 3

A) 2x(x-5)+3(x²-2)+(x+4)²-2(x-2)(x+2)= 2x² -10x + 3x² - 6 + x²+16 -2(x² +2x - 2x - 4) = 2x² -10x + 3x² - 6 + x²+16 -2x² -4x +4x + 8= 4x² - 10x +18

b) 4(3-x²)+4(x-1)²-3x(2-x)+(3-x)(3+x)= 12 -4x² +4(x²-2x+1) -6x +3x² + 9+3x-3x-x²= 12-4x² + 4x² -8x +4 -6x +3x² + 9+3x-3x-x² = 25 +2x² - 14x

c) (x-5)²-3(x-1)-(x+1)-(2x²-1)+x(2x-3)= x² -10x+25- 3x+3- x -1-2x²+1 +2x²-3x= x² - 17x +28

d)(4+x)(4-x)-2x(1-3x)+2(x+2)²-4(x²-1)= 16 -4x+4x -x²-2x+6x²+ 2(x²+4x+4)-4x²+4= 16-4x+4x -x²-2x+6x²+ 2x² +8x +8 -4x²+4 = 28 +6x +3x²