Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
, bạn nào biết thì giúp mình sửa nhé
a, Theo bài ra ta có:
\(=x^3-x-2x+2\)
\(=x\left(x^2-1\right)-2\left(x-1\right)\)
\(=x\left(x+1\right)\left(x-1\right)-2\left(x-1\right)\)
\(=\left(x-1\right)\left(x^2+x-2\right)\)
b, theo bài ra ta có:
\(=x^3-3x^2-\left(2x^2-6x\right)-\left(3x-9\right)\)
\(=x^2\left(x-3\right)-2x\left(x-3\right)-3\left(x-3\right)\)
\(=\left(x^2-2x-3\right)\left(x-3\right)\)
c,Theo bài ra ta có:
\(=x^3+5x^2+3x^2+15x+2x+10\)
\(=x^2\left(x+5\right)+3x\left(x+5\right)+2\left(x+5\right)\)
\(=\left(x+5\right)\left(x^2+3x+2\right)\)
\(=\left(x+5\right)\left(x^2+x+2x+2\right)=\left(x+5\right)\left(x\left(x+1\right)+2\left(x+1\right)\right)\)
\(=\left(x+5\right)\left(x+1\right)\left(x+2\right)\)
CHÚC BẠN HỌC TỐT...........
a) \(x^3-3x+2\)
= \(x^3-x^2+x^2-x-2x+2\)
= \(x^2\left(x-1\right)+x\left(x-1\right)-2\left(x-1\right)\)
= \(\left(x-1\right)\left(x^2+x-2\right)\)
= \(\left(x-1\right)\left(x^2+2x-x-2\right)\)
= \(\left(x-1\right)\left[x\left(x+2\right)-\left(x+2\right)\right]\)
= \(\left(x-1\right)\left(x+2\right)\left(x-1\right)\)
= \(\left(x-1\right)^2\left(x+2\right)\)
b) \(x^3-5x^2+3x+9\)
= \(x^3+x^2-6x^2-6x+9x+9\)
= \(x^2\left(x+1\right)-6x\left(x+1\right)+9\left(x+1\right)\)
= \(\left(x+1\right)\left(x^2-6x+9\right)\)
= \(\left(x+1\right)\left(x-3\right)^2\)
c) \(x^3+8x^2+17x+10\)
= \(x^3+x^2+7x^2+7x+10x+10\)
= \(x^2\left(x+1\right)+7x\left(x+1\right)+10\left(x+1\right)\)
= \(\left(x+1\right)\left(x^2+7x+10\right)\)
= \(\left(x+1\right)\left(x^2+2x+5x+10\right)\)
= \(\left(x+1\right)\left[x\left(x+2\right)+5\left(x+2\right)\right]\)
= \(\left(x+1\right)\left(x+2\right)\left(x+5\right)\)
d) \(x^3-3x^2+6x+4\)
Câu này đúng là sai đề rồi, mình sửa + làm bên dưới:
\(x^3+3x^2+6x+4\)
= \(x^3+x^2+2x^2+2x+4x+4\)
= \(x^2\left(x+1\right)+2x\left(x+1\right)+4\left(x+1\right)\)
= \(\left(x+1\right)\left(x^2+2x+4\right)\)
Học tốt nhé :))
Trong sách có mà bạn ( Ít nhất cũng thuộc chứ )
1. Bình phương của một tổng:
\(\left(a+b\right)^2=a^2+2ab+b^2\)
2. Bình phương của một hiệu:
\(\left(a-b\right)^2=a^2-2ab+b^2\)
3. Hiệu hai bình phương:
\(a^2-b^2=\left(a-b\right)\left(a+b\right)\)
4. Lập phương của một tổng:
\(\left(a+b\right)^3=a^3+3a^2b+3ab^2+b^3\)
5. Lập phương của một hiệu:
\(\left(a-b\right)^3=a^3-3a^2b+3ab^2-b^3\)
6. Tổng hai lập phương:
\(a^3+b^3=\left(a+b\right)\left(a^2-ab+b^2\right)=\left(a+b\right)^3-3a^2b-3ab^2=\left(a+b\right)^3-3ab\left(a+b\right)\)
7. Hiệu hai lập phương:
\(a^3-b^3=\left(a-b\right)\left(a^2+ab+b^2\right)=\left(a-b\right)^3+3a^2b-3ab^2=\left(a-b\right)^3+3ab\left(a-b\right)\)
Hok tốt
\(\left(x+y+z\right)^2-2\left(x+y+z\right)\left(x+y\right)+\left(x+y\right)^2\)
= \(\left[\left(x+y+z\right)-\left(x+y\right)\right]^2\)
= \(z^2\)
Ta có:(x + y + z)2 - 2(x + y + z) (x + y) + (x + y)2
=[(x+y+z)-(x+y)]2=z2
\(A=\left(x+1\right)^3-\left(x+3\right)^2\left(x+1\right)+4x^2+8\)
\(A=x^3+3x^2+3x+1-\left(x^2+6x+9\right)\left(x+1\right)+4x^2+8\)
\(A=x^3+3x^2+3x+1-\left(x^3+6x^2+9x+x^2+6x+9\right)+4x^2+8\)
\(A=x^3+3x^2+3x+1-x^3-6x^2-9x-x^2-6x-9+4x^2+8\)
\(A=\left(x^3-x^3\right)+\left(3x^2-6x^2-x^2+4x^2\right)+\left(3x-9x-6x\right)+\left(1-9+8\right)\)
\(A=-12x\)
\(B=\left(x-2\right)\left(x^2+2x+4\right)-\left(x+1\right)^3+3\left(x-1\right)\left(x+1\right)\)
\(B=x^3+2x^2+4x-2x^2-4x-8-\left(x^3+3x^2+3x+1\right)+3\left(x^2-1\right)\)
\(B=x^3+2x^2+4x-2x^2-4x-8-x^3-3x^2-3x-1+3x^2-3\)
\(B=\left(x^3-x^3\right)+\left(2x^2-2x^2-3x^2+3x^2\right)+\left(4x-4x-3x\right)+\left(-8-3-1\right)\)
\(B=-3x-12\)
Câu C tương tự.
Chúc bạn học tốt!!!
A = \(\left(x+1\right)^3-\left(x+3\right)^2.\left(x+1\right)+4x^2+8\)
A = \(\left(x+1\right)\left(x+1-x-3\right)\left(x+1+x+3\right)+4x^2+8\)
A = \(\left(x+1\right).\left(-2\right).\left(2x+4\right)+4x^2+8\)
A = \(\left(-2\right)\left(2x^2+4x+2x+4\right)+4x^2+8\)
A = \(\left(-2\right)\left(2x^2+6x+4\right)+4x^2+8\)
A = \(-4x^2-12x-8+4x^2+8=-12x\)
b) B = \(\left(x-2\right)\left(x^2+2x+4\right)-\left(x+1\right)^3+3\left(x-1\right)\left(x+1\right)\)
B = \(x^3-8-\left(x+1\right)\left(x^2+2x+1+3x-3\right)\)
B = \(x^3-8-\left(x+1\right)\left(x^2+5x-2\right)\)
B = \(x^3-8-x^3-5x^2+2x-x^2-5x+2\)
B = \(-6x^2-3x-6\)
a) \(x^2-6x+3\)
\(=x^2-2.x.3+9-6\)
\(=\left(x-3\right)^2-\left(\sqrt{6}\right)^2\)
\(=\left(x-3-\sqrt{6}\right)\left(x-3+\sqrt{6}\right)\)
b) \(9x^2+6x-8\)
\(=\left(3x\right)^2+2.3x+1-9\)
\(=\left(3x+1\right)^2-3^2\)
\(=\left(3x+1-3\right)\left(3x+1+3\right)\)
\(=\left(3x-2\right)\left(3x+4\right)\)
d) \(x^3+6x^2+11x+6\)
\(=x^3+3x^2+3x^2+9x+2x+6\)
\(=x^2\left(x+3\right)+3x\left(x+3\right)+2\left(x+3\right)\)
\(=\left(x+3\right)\left(x^2+3x+2\right)\)
\(=\left(x+3\right)\left(x^2+x+2x+2\right)\)
\(=\left(x+3\right)\left[x\left(x+1\right)+2\left(x+1\right)\right]\)
\(=\left(x+3\right)\left(x+1\right)\left(x+2\right)\)
e) \(x^3+4x^2-29x+24\)
\(=x^3+8x^2-4x^2-32x+3x+24\)
\(=x^2\left(x+8\right)-4x\left(x+8\right)+3\left(x+8\right)\)
\(=\left(x+8\right)\left(x^2-4x+3\right)\)
\(=\left(x+8\right)\left(x^2-3x-x+3\right)\)
\(=\left(x+8\right)\left[x\left(x-3\right)-\left(x-3\right)\right]\)
\(=\left(x+8\right)\left(x-3\right)\left(x-1\right)\)
a: \(9x^2-6x+3\)
\(=\left(9x^2-6x+1\right)+2\)
\(=\left(3x-1\right)^2+2\ge2\)
b: \(6x-x^2+1\)
\(=-\left(x^2-6x-1\right)\)
\(=-\left(x^2-6x+9-10\right)\)
\(=-\left(x-3\right)^2+10\le10\)
Và các bạn làm cho mình cả những bài mà mình đã gửi lên nữa nhé ! Thanks 
a) \(a^4+4\)
\(=a^4+4a^2+4-4a^2\)
\(=\left(a^2+2\right)^2+\left(2a\right)^2\)
\(=\left(a^2+2a+2\right)\left(a^2-2a+2\right)\)
b) \(\left(x+y+z\right)^3-x^3-y^3-z^3\)
\(=\left[\left(x+y\right)+z\right]^3-x^3-y^3-z^3\)
\(=\left(x+y\right)^3+z^3+3z\left(x+y\right)\left(x+y+z\right)-x^3-y^3-z^3\)
\(=x^3+y^3+3xy\left(x+y\right)+z^3+3z\left(x+y\right)\left(x+y+z\right)-x^3-y^3-z^3\)
\(=3\left(x+y\right)\left(xy+xz+yz+z^2\right)\)
\(=3\left(x+y\right)\left[x\left(y+z\right)+z\left(y+z\right)\right]\)
\(=3\left(x+y\right)\left(y+z\right)\left(z+x\right)\)
a: \(A=\left(x-5\right)\left(2x+3\right)-2x\left(x-3\right)\)
\(=2^{X2}+3x-10x-15-2x^2+6x\)
=-x-15
b: \(B=\left(12x-5\right)\left(4x-1\right)+\left(3x-7\right)\left(1-16x\right)\)
\(=48x^2-12x-20x+5+3x-48x^2-7+112x\)
\(=83x-2\)
a, \(x^2+4x+4=x^2+2x+2x+4\)
\(=x.\left(x+2\right)+2.\left(x+2\right)=\left(x+2\right)^2\)
b, \(4x^2-12x+9=4x^2-6x-6x+9\)
\(=2x.\left(2x-3\right)-3.\left(2x-3\right)=\left(2x-3\right)^2\)
c, \(x^3+8=x^3+2x^2-2x^2-4x+4x+8\)
\(=x^2.\left(x+2\right)-2x.\left(x+2\right)+4.\left(x+2\right)\)
\(=\left(x+2\right).\left(x^2-2x+4\right)\)
Chúc bạn học tốt!!!
1. x2 + 4x + 4 = (x + 2)2
2. 4x2 - 12x + 9 = (2x - 3)2
3. x3 + 8 = (x + 2)(x2 - 2x + 4)