Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
a,\(\left(a-b\right)\left(a+2b\right)-\left(b-a\right)\left(2a-b\right)-\left(a-b\right)\left(a+3b\right)\)
\(=\left(a-b\right)\left(a+2b\right)+\left(a-b\right)\left(2a-b\right)-\left(a-b\right)\left(a+3b\right)\)
\(=\left(a-b\right)\left(a+2b+2a-b-a-3b\right)\)
\(=\left(a-b\right)\left(2a-2b\right)\)
\(=\left(a-b\right)2\left(a-b\right)\)
\(=2\left(a-b\right)^2\)
b,\(\left(x+y\right)\left(2x-y\right)+\left(2x-y\right)\left(3x-y\right)-\left(y-2x\right)\)
\(=\left(x+y\right)\left(2x-y\right)+\left(2x-y\right)\left(3x-y\right)+\left(2x-y\right)\)
\(=\left(2x-y\right)\left(x+y+3x-y+1\right)\)
\(=\left(2x-y\right)\left(4x+1\right)\)
c,\(x^2\left(y-z\right)+y^2\left(z-x\right)+z^2\left(x-y\right)\)
\(=x^2y-x^2z+y^2z-y^2x+z^2\left(x-y\right)\)
\(=x^2y-y^2x-x^2z+y^2z+z^2\left(x-y\right)\)
\(=xy\left(x-y\right)-z\left(x^2-y^2\right)+z^2\left(x-y\right)\)
\(=xy\left(x-y\right)-z\left(x-y\right)\left(x+y\right)+z^2\left(x-y\right)\)
\(=\left(x-y\right)\left(xy-zx-zy+z^2\right)\)
\(=\left(x-y\right)\left(y-z\right)\left(x-z\right)\)
a: =(a^2-b^2)-(2a-2b)
=(a-b)(a+b)-2(a-b)
=(a-b)(a+b-2)
b: =(3x-3y)+5y(x-y)
=3(x-y)+5y(x-y)
=(x-y)(5y+3)
c: \(=\left(x+y\right)^2\left(x-y\right)+x\left(y-x\right)\)
=(x-y)*(x+y)^2-x(x-y)
=(x-y)[(x+y)^2-x]
d: \(=\left(x-y+4-2x-3y+1\right)\left(x-y+4+2x+3y-1\right)\)
=(-x-4y+5)(3x+2y+3)
e: =16-(x^2-4xy+4y^2)
=16-(x-2y)^2
=(4-x+2y)(4+x-2y)
g: =9x^2-6x+1-(3xy-y)
=(3x-1)^2-y(3x-1)
=(3x-1)(3x-y-1)
h: =(x-y)^3-z^3
=(x-y-z)[(x-y)^2+z(x-y)+z^2]
=(x-y-z)(x^2-2xy+y^2+xz-yz+z^2)
a) \(a^2-b^2-2a+2b\)
\(=\left(a^2-b^2\right)-\left(2a-2b\right)\)
\(=\left(a+b\right)\left(a-b\right)-2\left(a-b\right)\)
\(=\left(a-b\right)\left(a+b-2\right)\)
b) \(3x-3y-5x\left(y-x\right)\)
\(=\left(3x-3y\right)+5x\left(x-y\right)\)
\(=3\left(x-y\right)+5x\left(x-y\right)\)
\(=\left(5x+3\right)\left(x-y\right)\)
c) \(x\left(x+y\right)^2-y\left(x+y\right)^2+xy-x^2\)
\(=\left(x+y\right)^2\left(x-y\right)+\left(xy-x^2\right)\)
\(=\left(x+y\right)^2\left(x-y\right)-x\left(x-y\right)\)
\(=\left(x-y\right)\left(x^2+2xy+y^2-x\right)\)
d) \(\left(x-y+4\right)^2-\left(2x+3y-1\right)\)
\(=\left(x-y+4+2x+3y-1\right)\left(x-y+4-2x-3y+1\right)\)
\(=\left(3x+2y+3\right)\left(-x-4y+5\right)\)
Hai câu đầu tham khảo
Câu hỏi của Bangtan Sonyeondan - Toán lớp 8 - Học toán với OnlineMath
c) \(E=\left(x+a\right)\left(x+2a\right)\left(a+3a\right)\left(x+4a\right)+a^4\)
\(=\left(x+a\right)\left(x+4a\right)\left(x+2a\right)\left(a+3a\right)+a^4\)
\(=\left(x^2+5ax+4a^2\right)\left(a^2+5ax+6a^2\right)+a^4\)(1)
Đặt \(x^2+5ax+4a^2=t\)
\(\Rightarrow\left(1\right)=t\left(t+2a^2\right)+a^4\)
\(=t^2+2a^2t+a^4=\left(t+a^2\right)^2\)(2)
Mà \(x^2+5ax+4a^2=t\)
Nên \(\left(2\right)=\left(x^2+5ax+5a^2\right)^2\)
2
a
\(x+y+z=0\)
\(\Rightarrow x+y=-z\)
\(\Rightarrow\left(x+y\right)^3=\left(-z\right)^3\)
\(\Rightarrow x^3+y^3+3x^2y+3xy^2=-z^3\)
\(\Rightarrow x^3+y^3+z^3=3xy\left(x+y\right)=3xyz\)
b
Đặt \(a-b=x;b-c=y;c-a=z\Rightarrow x+y+z=0\)
Ta có bài toán mới:Cho \(x+y+z=0\).Phân tích đa thức thành nhân tử:\(x^3+y^3+z^3\)
Áp dụng kết quả câu a ta được:
\(\left(a-b\right)^3+\left(b-c\right)^3+\left(c-a\right)^3=3\left(a-b\right)\left(b-c\right)\left(c-a\right)\)
chuyển về dạng nguyên thể rồi tính thể chất khối lượng sau đó quay về đang tìm mũ của nhiều số làm ra rồi thì dễ lắm bạn ạ k minh nha
a)\(\left(x^2-2\right)\left(x^2+2x+2\right)\)
b)\(\left(x-1\right)\left(2x+1\right)\left(3x+7\right)\)
c)\(-2\left(x-4\right)\left(2x+1\right)\)
d)\(\left(x-5\right)\left(4x+1\right)\)
e)\(3\left(x-2\right)\left(3x-2\right)\)
g)\(2\left(a-b\right)^2\)
h)\(\left(xy-3\right)\left(5y^2-2z\right)\)
i)\(\left(4x+1\right)\left(2x-y\right)\)
l)\(abc^2\left(b-a\right)\left(b+c\right)\)
m)\(\left(x-y\right)\left(y-z\right)\left(x-z\right)\)
a)x+2a.(x-y)-y=(x-y)+2a(x-y)
=(x-y)(1+2a)
b)x^2-(a+b)x+ab=[x^2-(a+b)x]+a
=x(x-a-b)+a
1) (a - b)x - (b - a)y + a - b
= (a - b)x + (a - b)y + (a - b)
= (a - b)(x + y + 1)
2) (x - y + z)a + (y - x - z)b - x + y - z
= (x - y + z)a - (x - y + z)b - (x - y + z)
= (x - y + z)(a - b - 1)
3) (2a + 3)x - 2ay - 3y + 2a + 3
= (2a + 3)x - (2a + 3)y + (2a + 3)
= (2a + 3)(x - y + 1)
4) (a - b)x + by - ay - a +b
= (a - b)x - (a - b)y - (a - b)
= (a - b)(x - y - 1)