Question

Calculați:
a) (2x-3)²-x(x+1)=
b) (1-5x)²-(5x+1)(1-2x)=
c) 3(x-2)(x+2)-(1+3x)²=
d) (x+2-x²)²-(2+x²)²=
e) (4-x)(x-4)-(3-x)(x+3)=
f) 2(x-3)(4+x)-3(x-2)²=
g) 4-2(x-2)²+(2x-3)(3+2x)=
h) (1+x-x²)²+(3-x²)(x²+3)=
i) (3-x-x²)²+(x²+2x)²-2(x²-1)²=

Answer 1

a) (2x-3)²-x(x+1)=
=4x²-12x+9-x²-x=
=3x²-13x+9
b) (1-5x)²-(5x+1)(1-2x)=
=1-10x+25x²-(5x+1-10x²-2x)=
=1-10x+25x²-5x-1+10x²+2x=
=35x²-13x

c) 3(x-2)(x+2)-(1+3x)²=
=3(x²-4)-(1+9x²+6x)=
=3x²-12-1-9x²-6x=
=-6x²-6x-13

d) (x+2-x²)²-(2+x²)²=
=(x+2-x²-2-x²)(x+2-x²+2+x²)=
=(x-2x²)(x+4)=
=x²-2x³+4x-8x²=
=-2x³+4x-7x²


e) (4-x)(x-4)-(3-x)(x+3)=
=-(x-4)(x-4)-(3-x)(3+x)=
=-x²+8x-16-9+x²=
=8x-25

f) 2(x-3)(4+x)-3(x-2)²=
=2(4x-12+x²-3x)-3(x²-4x+4)=
=8x-24+2x²-6x-3x²+12x-12=
=-x²+14x-36

g) 4-2(x-2)²+(2x-3)(3+2x)=
=4-2(x²-4x+4)+(4x²-9)=
=4-2x²+8x-8+4x²-9=
=8x+2x²-13

h) (1+x-x²)²+(3-x²)(x²+3)=
=1+x²+x⁴+2x-2x²-2x³+9-x⁴=
=2x-x²-2x³+10=
=-2x³-x²+2x+10
 
i) (3-x-x²)²+(x²+2x)²-2(x²-1)²=
=9+x²+x⁴-6x-6x²+2x³+x⁴+4x³+4x²-2x⁴+4x²-2=
=7-6x+6x³+3x²=
= 6x³+ 3x²-6x+7

Answer 2

a) (2x-3)²-x(x+1)=4x²-12x+9-x²-x=3x²-13x+9

b) (1-5x)²-(5x+1)(1-2x)=1-10x+25x²-5x+10x²-1+2x=35x²-13x

c) 3(x-2)(x+2)-(1+3x)²=3(x²-4)-(1+6x+9x²)= -6x² -6x - 13

d) (x+2-x²)²-(2+x²)²=x²+2x-x³+2x+4-2x²-x³-2x²+x4-4-4x²-x4= -2x³-7x²+4x

e) (4-x)(x-4)-(3-x)(x+3)=4x-16-x²+4x-3x-9+x²+3x=8x-25

f) 2(x-3)(4+x)-3(x-2)²=8x+2x²-24-6x-3x²+12x-12= -x²+14x-36

g) 4-2(x-2)²+(2x-3)(2x+3)=4-2x²+8x-8+4x²-9=2x²+8x-13

h) (1+x-x²)²+(3-x²)(x²+3)=1+x-x²+x+x²-x³-x²-x³+x4+3x²+9-x4-3x²= -2x³-x²+2x+10

i) (3-x-x²)+(x²+2x)²-2(x²-1)²=9-3x-3x²-3x+x²+x³-3x²+x³+x4+x4+4x³+4x²-2x4+4x²-2=6x³+ 3x²-6x+7