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\(A=x^2-y^2-x+y\)
\(=\left(x^2-y^2\right)-\left(x-y\right)\)
\(=\left(x+y\right)\left(x-y\right)-\left(x-y\right)\)
\(=\left(x+y-1\right)\left(x-y\right)\)
\(B=ax-ab+b-x\)
\(=\left(ax-ab\right)-\left(x-b\right)\)
\(=a\left(x-b\right)-\left(x-b\right)\)
\(=\left(a-1\right)\left(x-b\right)\)
\(D=x^2-2xy+y^2-m^2+2mn-n^2\)
\(=\left(x^2+y^2-2xy\right)-\left(m^2+n^2-2mn\right)\)
\(=\left(x-y\right)^2-\left(m-n\right)^2\)
\(=\left(x-y-m+n\right)\left(x-y+m-n\right)\)
\(E=x^2-y^2-2yz-z^2\)
\(=x^2-\left(y^2+z^2+2yz\right)\)
\(=x^2-\left(y-z\right)^2\)
\(=\left(x+y-z\right)\left(z-y+z\right)\)
\(=>A=\left(x-y\right)\left(x+y\right)-\left(x-y\right)\\ =>A=\left(x-y\right)\left(x+y-1\right)\) ( 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
a) \(x\left(x-5\right)-4x+20=0\)
\(\Leftrightarrow x\left(x-5\right)-4\left(x-5\right)=0\)
\(\Leftrightarrow\left(x-4\right)\left(x-5\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x-4=0\\x-5=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=4\\x=5\end{cases}}\)
Vậy tập nghiệm của pt là \(S=\left\{4;5\right\}\)
b) \(x\left(x+6\right)-7x-42=0\)
\(\Leftrightarrow x\left(x+6\right)-7\left(x+6\right)=0\)
\(\Leftrightarrow\left(x-7\right)\left(x+6\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x-7=0\\x+6=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=7\\x=-6\end{cases}}\)
Vậy tập nghiệm của pt là \(S=\left\{-6;7\right\}\)
bÀI LÀM
a) x4+x3+2x2+x+1=(x4+x3+x2)+(x2+x+1)=x2(x2+x+1)+(x2+x+1)=(x2+x+1)(x2+1)
b)a3+b3+c3-3abc=a3+3ab(a+b)+b3+c3 -(3ab(a+b)+3abc)=(a+b)3+c3-3ab(a+b+c)
=(a+b+c)((a+b)2-(a+b)c+c2)-3ab(a+b+c)=(a+b+c)(a2+2ab+b2-ac-ab+c2-3ab)=(a+b+c)(a2+b2+c2-ab-ac-bc)
c)Đặt x-y=a;y-z=b;z-x=c
a+b+c=x-y-z+z-x=o
đưa về như bài b
d)nhóm 2 hạng tử đầu lại và 2hangj tử sau lại để 2 hạng tử sau ở trong ngoặc sau đó áp dụng hằng đẳng thức dề tính sau đó dặt nhân tử chung
e)x2(y-z)+y2(z-x)+z2(x-y)=x2(y-z)-y2((y-z)+(x-y))+z2(x-y)
=x2(y-z)-y2(y-z)-y2(x-y)+z2(x-y)=(y-z)(x2-y2)-(x-y)(y2-z2)=(y-z)(x2-2y2+xy+xz+yz)
a: \(=\left(x+2-y\right)\left(x+2+y\right)\)
c: \(=\left(x-y\right)^2\)
a.
\(=\left(x+1\right)^3-\left(3z\right)^3\)
\(=\left(x+1+3z\right)\left[\left(x+1\right)^2+3z\left(x+1\right)+9z^2\right]\)
\(=\left(x+3z+1\right)\left(x^2+2x+1+3zx+3z+9z^2\right)\)
b.
\(=\left(x-y\right)^2-z\left(x-y\right)\)
\(=\left(x-y\right)\left(x-y-z\right)\)
c.
\(=x^4-1+4x^2-4\)
\(=\left(x^2-1\right)\left(x^2+1\right)+4\left(x^2-1\right)\)
\(=\left(x^2-1\right)\left(x^2+5\right)\)
\(=\left(x-1\right)\left(x+1\right)\left(x^2+5\right)\)
a) Ta có: \(x^3+3x^2+3x+1-27z^3\)
\(=\left(x+1\right)^3-\left(3z\right)^3\)
\(=\left(x+1-3z\right)\left(x^2+2x+1+3xz+3z+9z^2\right)\)
b) Ta có: \(x^2-2xy+y^2-zx+yz\)
\(=\left(x-y\right)^2-z\left(x-y\right)\)
\(=\left(x-y\right)\left(x-y-z\right)\)
c) Ta có: \(x^4+4x^2-5\)
\(=x^4+4x^2+4-9\)
\(=\left(x^2+2\right)^2-3^2\)
\(=\left(x^2-1\right)\left(x^2+5\right)\)
\(=\left(x-1\right)\left(x+1\right)\left(x^2+5\right)\)
a) xy – 3x + 2y – 6
= (xy - 3x) + (2y - 6)
= x(y - 3) + 2(y - 3)
= (y - 3)(x + 2)
b) x2y + 4xy + 4y – y3
= y(x2 + 4x + 4 - y2)
= y[(x2 + 4x + 4) - y2]
= y[(x + 2)2 - y2]
= y(x + 2 + y)(x + 2 - y)
c) x2 + y2 + xz + yz + 2xy
= (x2 + 2xy + y2) + (xz + yz)
= (x + y)2 + z(x + y)
= (x + y)(x + y + z)
d) x3 + 3x2 – 3x – 1
= (x3 - 1) + (3x2 - 3x)
= (x - 1)(x2 + x + z) + 3x(x - 1)
= (x - 1)(x2 + 4x + 1)
a )
\(xy-3x+2y-6\)
\(=\left(xy+2y\right)-3x-6\)
\(=y\left(x+2\right)-3\left(x+2\right)\)
\(=\left(y-3\right)\left(x+2\right)\)
b )
\(x^2y+4xy+4y-y^3\)
\(=y\left(x^2+4x+4-y^2\right)\)
\(=y\left[\left(x+2\right)^2-y^2\right]\)
\(=y\left(x+2-y\right)\left(x+2+y\right)\)
c )
\(x^2+y^2+xz+yz+2xy\)
\(=\left(x+y\right)^2+z\left(x+y\right)\)
\(=\left(x+y\right)\left(x+y+z\right)\)
1) \(x^2-2xy+y^2-xz+yz\)
\(\Leftrightarrow\left(x^2-2xy+y^2\right)-\left(xz-yz\right)\)
\(\Leftrightarrow\left(x-y\right)^2-z\left(x-y\right)\)
\(\Leftrightarrow\left(x-y\right)\left(x-y-z\right)\)
2)\(x^2-y^2-x+y\)
\(\Leftrightarrow\left(x-y\right)\left(x+y\right)-\left(x-y\right)\)
\(\Leftrightarrow\left(x-y\right)\left(x+y+1\right)\)
\(a,x^2-2xy+y^2-xz+yz\)
\(=\left(x-y\right)^2-z\left(x-y\right)\)
\(=\left(x-y\right)\left(x-y-z\right)\)
\(b,x^2-y^2-x+y\)
\(=\left(x-y\right)\left(x+y\right)-\left(x-y\right)\)
\(=\left(x-y\right)\left(x+y-1\right)\)