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CẢM ƠN NHÌU 
6) c) x3 - x2 + x = 1
<=> x3 - x2 + x - 1 = 0
<=> (x3 - x2) + (x - 1) = 0
<=> x2 (x - 1) + (x - 1) = 0
<=> (x - 1) (x2 + 1) = 0
=> x - 1 = 0 hoặc x2 + 1 = 0
* x - 1 = 0 => x = 1
* x2 + 1 = 0 => x2 = -1 => x = -1
Vậy x = 1 hoặc x = -1
Bài 5:
a) Đặt \(A=\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)\)
\(\Rightarrow8A=\left(3^2-1\right)\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)\)
\(\Rightarrow8A=\left(3^4-1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)\)
\(\Rightarrow8A=\left(3^8-1\right)\left(3^8+1\right)\left(3^{16}+1\right)\)
\(\Rightarrow8A=\left(3^{16}-1\right)\left(3^{16}+1\right)\)
\(\Rightarrow8A=3^{32}-1\)
\(\Rightarrow A=\frac{3^{32}-1}{8}\)
b) (7x+6)2 + (5-6x)2 - (10-12x)(7x+6)
=(7x+6)2 + (5-6x)2 - 2(5-6x)(7x+6)
\(=\left(7x+6-5+6x\right)^2\)
\(=\left(13x+1\right)^2\)
a)x3-7x+6
=x3+0x2-7x+6
=x3-x2+x2-x-6x+6
=(x3-x2)+(x2-x)-(6x-6)
=x2(x-1)+x(x-1)-6(x-1)
=(x-1)(x2+x-6)
=(x-1)(x2-2x+3x-6)
=(x-1)[x(x-2)+3(x-2)]
=(x-1)(x+3)(x-2)
1) \(x^6-x^4-9x^3+9x^2\)
\(=x^2\left(x^4-x^2-9x+9\right)\)
\(=x^2\left[x^2\left(x^2-1\right)-9\left(x-1\right)\right]\)
\(=x^2\left(x-1\right)\left[x^2\left(x+1\right)-9\right]\)
\(=x^2\left(x-1\right)\left(x^3+x^2-9\right)\)
2) \(x^4-4x^3+8x^2-16x+16\)
\(=x^2\left(x^2+4\right)-4x\left(x^2+4\right)+4\left(x^2+4\right)\)
\(=\left(x^2+4\right)\left(x-2\right)^2\)
3) \(x^4-25x^2+20x-4=x^4+5x^3-2x^2-5x^3-25x^2+10x+2x^2+10x-4\)
\(=x^2\left(x^2+5x-2\right)-5x\left(x^2+5x-2\right)+2\left(x^2+5x-2\right)\)
\(=\left(x^2+5x-2\right)\left(x^2-5x+2\right)\)
4) \(5x\left(x-2y\right)+2\left(2y-x\right)^2\)\(=5x\left(x-2y\right)+2\left(x-2y\right)^2=\left(x-2y\right)\left(5x+2x-4y\right)=\left(x-2y\right)\left(7x-4y\right)\)
5) \(x^2\left(x^2-6\right)-x^2+9=x^4-7x^2+9\)
\(=x^4+x^3-3x^2-x^3-x^2+3x-3x^2-3x+9\)
\(=x^2\left(x^2+x-3\right)-x\left(x^2+x-3\right)-3\left(x^2+x-3\right)\)
\(=\left(x^2+x-3\right)\left(x^2-x-3\right)\)
6) \(7x\left(y-4\right)^2-\left(4-y\right)^3=7x\left(y-4\right)^2+\left(y-4\right)^3=\left(y-4\right)^2\left(7x+y-4\right)\)
7) \(x^3+2x^2-6x-27=x^3-3x^2+5x^2-15x+9x-27\)
\(=x^2\left(x-3\right)+5x\left(x-3\right)+9\left(x-3\right)=\left(x-3\right)\left(x^2+5x+9\right)\)
1.
\(x^2-22x+12\) : biểu thức không phân tích được thành nhân tử nữa.
2.
\(9x^2+6x+1=(3x)^2+2.3x.1+1^2=(3x+1)^2\)
3.
\(x^2-10x+2\): không p. tích được thành nhân tử.
4.
\(x^3+1=x^3+1^3=(x+1)(x^2-x+1)\)
5.
\(8x^3-27y^3=(2x)^3-(3y)^3=(2x-3y)[(2x)^2+(2x)(3y)+(3y)^2]\)
\(=(2x-3y)(4x^2+6xy+9y^2)\)
6.
\((x+3y)^2-(3y+1)^2=[(x+3y)-(3y+1)][(x+3y)+(3y+1)]\)
\(=(x-1)(x+6y+1)\)
7.
\(4y^2-36x^2=(2y)^2-(6x)^2=(2y-6x)(2y+6x)=4(y-3x)(y+3x)\)
8.
\(27-(x+4)^3=3^3-(x+4)^3=[3-(x+4)][3^2+3(x+4)+(x+4)^2]\)
\(=-(x+1)(37+x^2+11x)\)
9.
\(25x^2-10xy+y^2=(5x)^2-2.5x.y+y^2=(5x-y)^2\)
10.
\(9x^6-12x^7+4x^8=x^6(9-12x+4x^2)=x^6[3^2-2.3.2x+(2x)^2]\)
\(=x^6(3-2x)^2\)
bạn hỏi từng câu 1 lần thôi cũng đc hỏi 1 lần 17 câu thì thánh nào vô kiên nhẫn trả lời hết đc ^^
1 ) x3 - 2x2 + x
= x( x2 - 2x + 1 )
= x ( x-1)2
2) 4x3 - 25x
= x ( 4x2 - 25)
= x( 2x-5) ( 2x +5)
11) \(x^2-y^2-4x+4\)
\(=\left(x^2-4x+4\right)-y^2\)
\(=\left(x-2\right)^2-y^2\)
\(=\left(x-y-2\right)\left(x+y-2\right)\)
13) \(x^4+4=x^4+4x^2+4-4x^2\)
\(=\left(x^2+2\right)^2-4x^2\)
\(=\left(x^2-2x+2\right)\left(x^2+2x+2\right)\)
\(x^3-x^2-5x+125\)
\(=\left(x+5\right)\left(x^2-5x+25\right)-x\left(x+5\right)\)
\(=\left(x+5\right)\left(x^2-5x+25-x\right)\)
\(=\left(x+5\right)\left(x^2-6x+25\right)\)
\(x^6-x^4-9x^3+9x^2\)
\(=x^4\left(x^2-1\right)-9x^2\left(x-1\right)\)
\(=x^4\left(x-1\right)\left(x+1\right)-9x^2\left(x-1\right)\)
\(=x^2\left(x-1\right)\left[x^2\left(x+1\right)-9\right]\)
\(=x^2\left(x-1\right)\left(x^3+x^2-9\right)\)
\(x^4-4x^3+8x^2-16x+16\)
\(=\left(x^2+4\right)^2-4x\left(x^2+4\right)\)
\(=\left(x^2+4\right)\left(x^2+4-4x\right)\)
\(=\left(x^2+4\right)\left(x-2\right)^2\)
\(3a^2-6ab+3b^2-12c^2\)
\(=3\left(a^2-2ab+b^2-4c^2\right)\)
\(=3\left[\left(a-b\right)^2-\left(2c\right)^2\right]\)
\(=3\left(a-b+2c\right)\left(a-b-2c\right)\)
Bài 1:
a: \(6x^2-11x+3\)
\(=6x^2-9x-2x+3\)
\(=3x\left(2x-3\right)-\left(2x-3\right)\)
\(=\left(2x-3\right)\left(3x-1\right)\)
b: \(2x^2+3x-27\)
\(=2x^2+9x-6x-27\)
\(=x\left(2x+9\right)-3\left(2x+9\right)\)
\(=\left(2x+9\right)\left(x-3\right)\)
c: \(x^2-10x+24\)
\(=x^2-4x-6x+24\)
\(=x\left(x-4\right)-6\left(x-4\right)\)
\(=\left(x-4\right)\left(x-6\right)\)
d: \(49x^2+28x-5\)
\(=49x^2+28x+4-9\)
\(=\left(7x+2\right)^2-9\)
\(=\left(7x-1\right)\left(7x+5\right)\)
e: \(2x^2-5xy-3y^2\)
\(=2x^2-6xy+xy-3y^2\)
\(=2x\left(x-3y\right)+y\left(x-3y\right)\)
\(=\left(x-3y\right)\left(2x+y\right)\)
đăng ít 1 thôi
1. 8 - 12x + 6x2 - x3
= 23 - 3.22.x + 3.x2.2 - x3
=(2-x)3
2. 125x3 - 75x2 +15x - 1
=(5x)3 - 3.(5x)2.1 + 3.5x.12 - 13
=(5x - 1)3
3, 4 (sai đề)
5. x3 + 2x2 - 6x - 27
=(x3 - 27) + (2x2 - 6x)
=(x3 - 33) + (2x2 - 6x)
=(x -3)(x2 + 3x + 9) + 2x(x-3)
=(x-3)(x2 + 3x +9 +2x)
=(x-3)(x2 + 5x +9)
6. 12x3 + 4x2- 27x -9
=(12x3 + 4x2) - (27x + 9)
=4x2(3x + 1) - 9(3x +1)
=(3x -1)(4x2 -9)
=(3x-1)(2x-3)(2x+3)
7) 4x3 + 4x2 - x2 - x 8) x6 - x4 - 9x3 +9x2
=(4x3 + 4x2) - (x2 - x) =x4(x2 - 1) - 9x2(x - 1)
=4x2(x + 1) - x(x+1) =x4(x-1)(x+1) - 9x2(x-1)
=(x+1)(4x2 - x) =(x-1)(x5 +x4 - 9x2)
=4x(x-1)(x+1) =x2(x-1)(x3+x2-9)
9) x4 - 4x3 + 8x2 -16x + 16 10) 3a2 - 6ab + 3b2 -12c2
=(x4 + 8x2 +16) - (4x3 + 16x) =3(a2 - 2ab + b2 - 4c2)
=(x2 + 4)2 - 4x(x2 +4) =3[(a-b)2 - (2c)2]
=(x2 + 4)(x2 +4 - 4x) =3(a-b-2c)(a-b+2c)
=(x2 + 4)(x -2)2
11) a2 + 2ab + b2 - ac - bc
= (a +b)2 -c(a+b)
=(a + b)(a + b - c)
12) ac - bc - a2 + 2ab - b2
=c(a-b) -(a-b)2
=(a-b)(c-a+b)
13) (x - y + 5)2 - 2(x - y + 5).1 + 12
=(x - y + 5 -1)2
=(x - y + 4)2
14) x8 + x7 + 1
=x8 + x7 + 1 +x2 +x - x2 - x
=(x8 - x2) + (x7 - x) + (x2 +x +1)
=x2(x6 - 1) + x(x6 - 1) + (x2 + x + 1)
=x2(x3 - 1)(x3 + 1) +x (x3 - 1)(x3 + 1) + (x2 +x +1)
=x2(x-1)(x2 + x + 1)(x3 + 1) + x(x-1)(x2 + x + 1)(x3 + 1) +(x2 + x +1)
=(x2 + x +1)[ x2(x-1)(x3 + 1) + x(x-1)(x3 +1) +1]
=(x2 + x + 1)(x6 - x4 + x3 - x +1)
15) x8 + x4 +1
=x8 + 2x4 - x4 +1
=[(x4)2 + 2.x4.1 +12] - (x2)2
=(x4 +1)2 -(x2)2
=(x4 + 1 - x2)(x4 + 1 +x2)
=(x4 - x2 +1)(x4 + 2x2 +1 - x2)
=(x4 - x2 +1)[(x2+1)2 - x2]
=(x4 - x2 +1)(x2 - x+1)(x2 +x +1)
16) x5 + x + 1
=x5 +x +1 +x2 - x2
=(x5 - x2) + (x2 + x + 1)
=x2(x3 -1) + (x2 +x +1)
=x2(x-1)(x2+x+1) + (x2+x+1)
=(x2 +x+1)(x3- x2 +1)
17) x3 + x2 + 4
=x3 + 2x2 - x2 - 2x +2x + 4
=x2(x+2) - x(x+2) +2(x+2)
=(x+2)(x2 - x +2)
18) x4 + 2x2 - 24
=(x2)2 + 2.x2.1 +12 -25
=(x2 + 1) - 52
=(x2 +1 -5)(x2 +1 +5)
=(x2- 4)(x2 +6)
=(x-2)(x+2)(x2+6)
19) x3 - 2x - 4
=x3 - 2x2 + 2x2 - 4x + 2x -4
=x2(x-2) + 2x(x-2) + 2(x-2)
=(x-2)(x2+2x+2)
20)x2 + 4x + 3
=x2 + 2.x.2 + 22 -1
=(x+2)2 -12
=(x+2-1)(x+2+1)
=(x+1)(x+3)
c sai đề
1)\(8-12x+6x^2-x^3\)
\(=-\left(x^3-6x^2+12x-8\right)\)
\(=-\left(x-2\right)^3\)
2)\(15x^3-75x^2+15x-1\)
\(=\left(5x-1\right)^3\)
4)
sao câu này cũng sai đề thế mắt m` lé à
giải nhanh hộ mình với mai mình phải nộp bài rồi
viết lại đề rồi gửi link lại qua tin nhắn đi tối t giải cho
bạn ơi, mình xem qua có mấy cái sai đề rồi nhá, bạn xem lại rồi gửi cho mình, mình làm hết cho nếu sửa lại thì mình làm đc hết cho bạn rồi, vì nó đơn giản mà :))
câu 7,8,9,10 đống thẳng xuống mà nhìn