K
Khách

Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.

23 tháng 9 2020

a) \(\left(x+a\right)\left(x+b\right)\left(x+c\right)\)

\(=\left[x^2+\left(a+b\right)x+ab\right]\left(x+c\right)\)

\(=x^3+\left(a+b+c\right)x^2+\left(ab+bc+ca\right)x+abc\)

b) \(a^3+b^3+c^3-3abc\)

\(=\left(a+b\right)^3-3ab\left(a+b\right)+c^3-3abc\)

\(=\left(a+b+c\right)\left[\left(a+b\right)^2-\left(a+b\right)c+c^2\right]-3ab\left(a+b+c\right)\)

\(=\left(a+b+c\right)\left(a^2+2ab+b^2-ca-bc+c^2-3ab\right)\)

\(=\left(a+b+c\right)\left(a^2+b^2+c^2-ab-bc-ca\right)\)

c) \(a^2\left(b-c\right)+b^2\left(c-a\right)+c^2\left(a-b\right)\)

\(=a^2\left(b-c\right)+b^2c-ab^2+c^2a-bc^2\)

\(=a^2\left(b-c\right)+bc\left(b-c\right)-a\left(b-c\right)\left(b+c\right)\)

\(=\left(b-c\right)\left(a^2+bc-ab-ca\right)\)

\(=\left(a-b\right)\left(b-c\right)\left(c-a\right)\)

23 tháng 9 2020

Nhầm đoạn cuối là \(=\left(a-b\right)\left(b-c\right)\left(a-c\right)\)

9 tháng 2 2017

Bài 3a)

\(a+b+c=0\Leftrightarrow a+b=-c\Leftrightarrow a^3+b^3+3ab\left(a+b\right)=-c^3\)

\(\Leftrightarrow a^3+b^3+c^3=-3ab\left(a+b\right)\)

mà \(a+b=-c\Rightarrow a^3+b^3+c^3=3abc\)

7 tháng 7 2016

\(A=x^2-y^2-x+y\)

\(=\left(x^2-y^2\right)-\left(x-y\right)\)

\(=\left(x+y\right)\left(x-y\right)-\left(x-y\right)\)

\(=\left(x+y-1\right)\left(x-y\right)\)

\(B=ax-ab+b-x\)

\(=\left(ax-ab\right)-\left(x-b\right)\)

\(=a\left(x-b\right)-\left(x-b\right)\)

\(=\left(a-1\right)\left(x-b\right)\)

\(D=x^2-2xy+y^2-m^2+2mn-n^2\)

\(=\left(x^2+y^2-2xy\right)-\left(m^2+n^2-2mn\right)\)

\(=\left(x-y\right)^2-\left(m-n\right)^2\)

\(=\left(x-y-m+n\right)\left(x-y+m-n\right)\)

\(E=x^2-y^2-2yz-z^2\)

\(=x^2-\left(y^2+z^2+2yz\right)\)

\(=x^2-\left(y-z\right)^2\)

\(=\left(x+y-z\right)\left(z-y+z\right)\)

7 tháng 7 2016

 \(=>A=\left(x-y\right)\left(x+y\right)-\left(x-y\right)\\ =>A=\left(x-y\right)\left(x+y-1\right)\) ( dấu phía sau bị lỗi nha )

\(=>B=a\left(x-b\right)-\left(x-b\right)\\ =>B=\left(x-b\right)\left(a-1\right)\)

\(=>C=\left(a+b+c\right)\left(3x^2+36xy+108y^2\right)\)

\(=>C=3\left(a+b+c\right)\left(x^2+12xy+36y^2\right)\\ =>C=3\left(a+b+c\right)\left(x+6y\right)^2\)

\(\Rightarrow D=\left(x-y\right)^2-\left(m^2-2mn+n^2\right)\\ =>D=\left(x-y\right)^2-\left(m-n\right)^2\)

\(=>D=\left(x-y+m-n\right)\left(x-y-m+n\right)\)

\(=>E=x^2-\left(y^2+2yz+z^2\right)\\ =>E=x^2-\left(y+z\right)^2\)

\(=>E=\left(x-y-z\right)\left(x+y+z\right)\)

T I C K ủng hộ nha

CHÚC BẠN HỌC TỐT

21 tháng 8 2017

\(a,3x^2+2x-1\)

\(\Leftrightarrow3x^2+3x-x-1\)

\(\Leftrightarrow3x\left(x+1\right)-\left(x+1\right)\)

\(\Leftrightarrow\left(x+1\right)\left(3x-1\right)\)

\(b,x^3+6x^2+11x+6\)

\(\Leftrightarrow x^3+3x^2+3x^2+9x+2x+6\)

\(\Leftrightarrow x^2\left(x+3\right)+3x\left(x+3\right)+2\left(x+6\right)\)

\(\Leftrightarrow\left(x+3\right)\left(x^2+3x+2\right)\)

\(\Leftrightarrow\left(x+3\right)\left(x+1\right)\left(x+2\right)\)

\(c,x^4+2x^2-3\)

\(\Leftrightarrow x^4-x^3+x^3-x^2+3x^2-3\)

\(\Leftrightarrow x^3\left(x-1\right)+x^2\left(x-1\right)+3\left(x-1\right)\left(x+1\right)\)

\(\Leftrightarrow\left(x-1\right)\left(x^3+x^2+3x+3\right)\)

\(\Leftrightarrow\left(x-1\right)\left(x+1\right)\left(x+3\right)\)

\(d,ab+ac+b^2+2bc+c^2\)

\(\Leftrightarrow a\left(b+c\right)+\left(b+c\right)^2\)

\(\Leftrightarrow\left(b+c\right)\left(a+b+c\right)\)

21 tháng 8 2017

3x^2+2x-1=3x^2+3x-x-1=3x(x+1)-(x+1)=(x+1)(3x-1)

x^4+2x^2-3=x^4+3x^2-x^2 -3=x^2(x^2+3)-(x^2+3)=(x^2+3)(x^2-1)

  1.