5)
a)
6x(2x+5)+5(2x+5)=
12x²+30x+10x+25=
12x²+(30x+10x)+25=
12x²+40x+25
b)
7x(5x+3)+14(5x+3)=
35x²+21x+70x+42=
35x²+(21x+70x)+42=
35x²+91x+42
c)
12x(2x-1)-4(2x-1)=
24x²-12x-8x+4=
24x²+(-12x-8x)+4=
24x²-20x+4
d)
12(x+3)²-6x(x+3)=
12x²+72x+108-6x²-18x=
(12x²-6x²)+(72x-18x)+108=
6x²+54x+108
e)
18x(3x-1)-6(3x-1)²=
54x²-18x-54x²+36x-6=
(54x²-54x²)+(-18x+36x)-6=
18x-6
f)
24x(4x-3)-8(4x-3)=
96x²-72x-32x+24=
96x²+(-72x-32x)+24=
96x²-104x+24
8)
a)
5x(x+2)+(x+2)²-3(x+2)=
5x²+10x+x²+2x×2+2²-3x-6=
5x²+10x+x²+4x+4-3x-6=
(5x²+x²)+(10x+4x-3x)+(4-6)=
6x²+11x-2
b)
(x+1)(x+2)+4(x+1)²-4x(x+1)=
x²+2x+x+2+4x²+8x+4-4x²-4x=
(x²+4x²-4x²)+(2x+x+8x-4x)+(2+4)=
x²+7x+6
c)
(x+2)(3x-7)-(x+2)(4x-2)+3(x+2)=
3x²-7x+6x-14-4x²+2x-8x+4+3x+6=
(3x²-4x²)+(-7x+6x+2x-8x+3x)+(-14+4+6)=
-x²-4x-4
d)
(2x-1)²-(3x+2)(2x-1)+6x(2x-1)=
(2x)²-2×2x+1-6x²+3x-4x+2+12x²-6x=
2²x²-2×2x+1-6x²+3x-4x+2+12x²-6x=
4x²-4x+1-6x²+3x-4x+2+12x²-6x=
(4x²-6x²+12x²)+(-4x+3x-4x-6x)+(1+2)=
10x²-11x+3
e)
(5x-4)(3x-2)²-(3x-2)³+2(x+4)(3x-2)²=
45x³-60x²+20x-36x²+48x-16-27x³+36x²-12x+18x²-24x+8+18x³-24x²+8x+72x²-96x+32=
(45x³-27x³+18x³)+(-60x²-36x²+36x²+18x²-24x²+72x²)+(20x+48x-12x-24x+8x-96x)+(-16+8+32)=
36x³-60x²+18x²-24x²+72x²-56x+24=
36x³+(-60x²+18x²-24x²+72x²)-56x-24=
36x³+6x²-56x+24
