Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
\(ab\left(x^2-y^2\right)-xy\left(a^2-b^2\right)\)
\(=abx^2-aby^2-xya^2+b^2xy\)
\(=\left(abx^2-xya^2\right)+\left(b^2xy-aby^2\right)\)
\(=ax\left(bx-ay\right)+by\left(bx-ay\right)\)
\(=\left(ax+by\right)\left(bx-ay\right)\)
a)\(x^4+x^3+x+1=x^3\left(x+1\right)+\left(x+1\right)=\left(x+1\right)\left(x^3+1\right)=\left(x+1\right)^2\left(x^2-x+1\right)\)
b)\(x^4-x^3-x^2+1=\left(x^4-x^3\right)-\left(x^2-1\right)=x^3\left(x-1\right)-\left(x-1\right)\left(x+1\right)\)
\(=\left(x-1\right)\left(x^3-x-1\right)\)
c)\(x^2y+xy^2-x-y=xy\left(x+y\right)-\left(x+y\right)=\left(xy-1\right)\left(x+y\right)\)
Ta có : x3 + 2x2 + x
= x3 + x2 + x2 + x
= x2(x + 1) + x(x + 1)
= (x2 + x) (x + 1)
= x(x + 1)(x + 1)
a/ (x-a)^4 - (x+a)^4
=((x-a)^2)^2 - ((x+a)^2)^2
=(x^2 - 2xa + a^2)^2 - (x^2 +2xa+a^2)^2
=(x^2-2xa+a^2-x^2-2xa-a^2)(x^2-2xa+a^2+x^2+2xa+a^2)
=-4xa(2x^2+2a^2)
b/ x^4 –y^2(2x-y)^2
=(x^2)^2-(y(2x-y)^2
=(x^2)^2-(2xy-y^2)^2
=(x^2-2xy+y^2)(x^2+2xy+y^2)
=(x-y)^2 (x+y)^2
c/(xy+4)^2- 4(x+y)^2
=(xy+4)^2- (2x+2y)^2
=(xy+y-2x-2y)(xy+y+2x+2y)
=(xy-y+2x)(xy+3y+2x)
\(\left(xy+1\right)^2-\left(x+y\right)^2\)
\(\left(xy+1-x-y\right)\left(xy+1+x+y\right)\)
Câu a) dễ, ko làm
b) \(x^2y^2+1-x^2-y^2\)
\(=x^2\left(y^2-1\right)-\left(y^2-1\right)\)
\(=\left(x^2-1\right)\left(y^2-1\right)\)
\(=\left(x+1\right)\left(x-1\right)\left(y+1\right)\left(y-1\right)\)
Câu c) đề sai
Câu c) ,đề đúng nek
\(bc\left(b+c\right)+ac\left(c-a\right)-ab\left(a+b\right)\)
\(=bc\left(b+c\right)+ac\left[\left(b+c\right)-\left(a+b\right)\right]-ab\left(a+b\right)\)
\(=bc\left(b+c\right)+ac\left(b+c\right)-ac\left(a+b\right)-ab\left(a+b\right)\)
\(=\left(b+c\right)\left(bc+ac\right)-\left(a+b\right)\left(ac+ab\right)\)
\(=\left(b+c\right)c\left(a+b\right)-\left(a+b\right)a\left(b+c\right)\)
\(=\left(b+c\right)\left(a+b\right)\left(c-a\right)\)
1) a) \(x^3-2x^2y+xy^2-25x=x\left(x^2-2xy+y^2-25\right)\)
\(=x\left[\left(x-y\right)^2-5^2\right]=x\left(x-y-5\right)\left(x-y+5\right)\)
b)\(x^2-y^2-2x-2y=\left(x^2-2x+1\right)-\left(y^2+2y+1\right)=\left(x-1\right)^2-\left(y+1\right)^2\)
\(=\left(x-1-y-1\right)\left(x-y+y+1\right)=\left(x-y-2\right)\left(x+1\right)\)
\(ab\left(x^2-y^2\right)-xy\left(a^2-b^2\right)\)
\(=abx^2-aby^2-xya^2+b^2xy\)
\(=\left(abx^2-xya^2\right)+\left(b^2xy-aby^2\right)\)
\(=ax\left(bx-ay\right)+by\left(bx-ay\right)\)
\(=\left(ax+by\right)\left(bx-ay\right)\)