Đáp án:
Giải thích các bước giải:
1)
A=(x-1)³+(1-x)³-3x(x+1)
=(x-1)(x-1)(x-1)+(1-x)(1-x)(1-x)-3x.x-3x.1
=x(x-1)-1(x-1).(x-1)+1(1-x)-x(1-x)(1-x)-3x²-3x
=x²-x-x+1.(x-1)+1-x-x+x².(1-x)-3x²-3x
=x²-x-x+x-1+1-x-x+x²-x²x-3x²-3x
=x²-x-x+x-1+1-x-x+x²-x³-3x²-3x
=(x²+x²-3x²)+(-x-x+x-x-x-3x)+(-1+1)-x³
=-x²-6x-x³
B=(2x-1)²-(1-2x)²
=(2x-1)(2x-1)-(1-2x)(1-2x)
=2x(2x-1)-1(2x-1)-1(1-2x)+2x(1-2x)
=4x²-2x-2x+1-1+2x+2x-4x²
=(4x²-4x²)+(-2x-2x+2x+2x)+(1-1)
=0
C=(a-b+c)²-(a+b-c)²
=(a-b+c)(a-b+c)-(a+b-c)(a+b-c)
=a(a-b+c)-b(a-b+c)+c(a-b+c)-a(a+b-c)-b(a+b-c)+c(a+b-c)
=a²-ab+ac-ab+b²-bc+ac-bc+c²-a²-ab+ac-ab-b²+bc+ac+bc-c²
=(a²-a²)+(-ab-ab-ab-ab)+(ac+ac+ac+ac)+(b²-b²)+(-bc-bc+bc+bc)+(c²-c²)
=-4ab+4ac
2)
a, 4x²-36=0
4x²=0+36
4x²=36
x²=36:4
x²=9
Mà: 9=3²
=>x=3
b, x³-3x²+3x-1=0
x³ - x² - 2x² + 2x + x - 1=0
x²(x - 1) -2x ( x-1) +1(x-1)=0
(x² - 2x +1) (x-1)=0
(x-1)² (x - 1)=0
(x - 1)³=0
=>x-1=0
x=1
c, (x-2)³-x³+6x²=5
(x-2)(x-2)(x-2)-x³+6x²=5
(x-2)(x² - 2x - 2x +4)-x³+6x²=5
(x-2)(x² - 4x +4)-x³+6x²=5
x(x² - 4x +4) - 2(x² - 4x +4)-x³+6x²=5
x³ - 4x²+4x - 2x² - 8x +8-x³+6x²=5
(x³-x³)+(- 4x²- 2x²+6x²)+(4x - 8x )+8=5
-4x+8=5
-4x=5-8
-4x=-3
x=$\frac{3}{4}$
4)M=(2x+3)(4x²-6x+9)-8x(x²+2)+16x+5
=2x(4x²-6x+9)+3(4x²-6x+9)-8x³-16x+16x+5
=8x³-12x²+18x+12x²-18x+27-8x³-16x+16x+5
=(8x³-8x³)+(-12x²+12x²)+(18x-18x)+(-16x+16x)+(27+5)
=32
=> M không phụ thuộc vào biến
