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\(e,-5x+x^2-14\)
\(=x^2+2x-7x-14\)
\(=x\left(x+2\right)-7\left(x+2\right)\)
\(=\left(x+2\right)\left(x-7\right)\)
\(f,x^3+8+6x\left(x+2\right)\)
\(=\left(x+2\right)\left(x^2+2x+4\right)+6x\left(x+2\right)\)
\(=\left(x+2\right)\left(x^2+8x+4\right)\)
\(g,15x^2-7xy-2y^2\)
\(=15x^2+3xy-10xy-2y^2\)
\(=3\left(5x+y\right)-2y\left(5x+y\right)\)
\(=\left(5x+y\right)\left(3-2y\right)\)
\(h,3x^2-16x+5\)
\(=3x^2-x-15x+5\)
\(=x\left(3x-1\right)+5\left(3x-1\right)\)
\(=\left(3x-1\right)\left(x+5\right)\)
\(a,x^3+2x^2y+xy^2=x\left(x^2+2xy+y^2\right)\)
\(=x\left(x+y\right)^2\)
\(b,4x^2-9y^2+4x-6y\)
\(=4x^2+4x+1-\left(9y^2+6y+1\right)\)
\(=\left(2x+1\right)^2-\left(3y+1\right)^2\)
\(=\left(2x-3y\right)\left(2x+3y+2\right)\)
\(c,-x^2+5x+2xy-5y-y^2\)
\(=-\left(x^2-2xy+y^2\right)+5\left(x-y\right)\)
\(=-\left(x-y\right)^2+5\left(x-y\right)\)
\(=\left(x-y\right)\left(y-x+5\right)\)
\(d,x^2+4x-12\)
\(=x^2-2x+6x-12\)
\(=x\left(x-2\right)+6\left(x-2\right)\)
\(=\left(x-2\right)\left(x+6\right)\)
a) \(12x^5y+24x^4y^2+12x^3y^3\)
\(=12x^3y\left(x^2+2xy+y^2\right)\)
\(=12x^3y\left(x+y\right)^2\)
b) \(x^2-2xy-4+y^2\)
\(=\left(x-y\right)^2-2^2\)
\(=\left(x-y-2\right)\left(x-y+2\right)\)
g) \(12xy-12xz+3x^2y-3x^2z\)
\(=12x\left(y-z\right)+3x^2\left(y-z\right)\)
\(=3x\left(4+x\right)\left(y-z\right)\)
e) \(16x^2-9\left(x^2+2xy+y^2\right)\)
\(=\left(4x\right)^2-\left[3\left(x+y\right)\right]^2\)
\(=\left(4x-3\left(x+y\right)\right)\left(4x+3\left(x+y\right)\right)\)
\(=\left(x+y\right)\left(7x+y\right)\)
d) làm tương tự như phần g chỉ khác là phải nhóm( nhóm xen kẽ), phần f cũng vậy
1.a)\(3x^5\left(x+1\right)-9x\left(x+1\right)\)
\(=3x\left(x+1\right)\left(x^4-3\right)\)
b)\(4x^2\left(x-2y\right)-20x\left(2y-x\right)\)
\(=4x^2\left(x-2y\right)+20x\left(x-2y\right)\)
\(=4x\left(x-2y\right)\left(x+5\right)\)
c)\(3x^2y^2\left(a-b+c\right)+2xy\)
\(=xy\left[3xy\left(a-b+c\right)+2\left(b-a-c\right)\right]\)
\(=xy\left[3xy\left(a-b+c\right)-2\left(a-b+c\right)\right]\)
\(=xy\left(3xy-2\right)\left(a-b+c\right)\)
d)\(\left(a-b\right)^2-\left(b-a\right)\)
\(=\left(a-b\right)^2+\left(a-b\right)\)
\(=\left(a-b\right)\left(a-b+1\right)\)
2.a) \(x^3+4x=0\)
\(\Leftrightarrow x\left(x^2+4\right)=0\)
\(\Rightarrow x=0\)(vì x2+4>0)
b)\(x\left(x-6\right)+10\left(6-x\right)=0\)
\(\Leftrightarrow x\left(x-6\right)-10\left(x-6\right)=0\)
\(\Leftrightarrow\left(x-6\right)\left(x-10\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-6=0\\x-10=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=6\\x=10\end{matrix}\right.\)
c)\(\left(x+2\right)^2=x+2\)
\(\Leftrightarrow\left(x+2\right)^2-\left(x+2\right)=0\)
\(\Leftrightarrow\left(x+2\right)\left(x+2-1\right)=0\)
\(\Leftrightarrow\left(x+2\right)\left(x+1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x+2=0\\x+1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-2\\x=-1\end{matrix}\right.\)
d)\(x\left(x+7\right)=4x+28\)
\(\Leftrightarrow x\left(x+7\right)=4\left(x+7\right)\)
\(\Leftrightarrow x\left(x+7\right)-4\left(x+7\right)=0\)
\(\Leftrightarrow\left(x-4\right)\left(x+7\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-4=0\\x+7=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=4\\x=-7\end{matrix}\right.\)
Câu 2 nha
\(a,x^4+2x^3+x^2\)
\(=x^2\left(x^2+2x+1\right)\)
\(=x^2\left(x+1\right)^2\)
\(c,x^2-x+3x^2y+3xy^2+y^3-y\)
\(=\left(x^3+3x^2y+3xy^2+y^3\right)-\left(x+y\right)\)
\(=\left(x+y\right)^3-\left(x+y\right)\)
\(=\left(x+y\right)\left(x^2+2xy+y^2-1\right)\)
\(x^3+8y^3+2xy^2+x^2y\)
\(=x^3+2x^2y-x^2y-2xy^2+4xy^2+8y^3\)
\(=x^2\left(x+2y\right)-xy\left(x+2y\right)+4y^2\left(x+2y\right)\)
\(=\left(x+2y\right)\left(x^2-xy+4y^2\right)\)
Ta có ; x2 - 11x + 24
= x2 - 3x - 8x + 24
= x(x - 3) - (8x - 24)
= x(x - 3) - 8(x - 3)
= (x - 3)(x - 8)
a, \(3x^2\left(x+1\right)-2\left(x+1\right)\)\(=\left(x+1\right)\left(3x^3-2\right)\)
b, \(4x^2\left(x-2y\right)-20x\left(2y-x\right)\)
\(=4x^2\left(x-2y\right)-20x\left[-\left(x-2y\right)\right]\)
\(=4x^2\left(x-2y\right)+20x\left(x-2y\right)\)
\(=\left(4x^2+20x\right)\left(x-2y\right)\)
\(=\left(4x^2+20x\right)\left(x-2y\right)\)
\(=4x\left(x+5\right)\left(x-2y\right)\)
c, \(3x^2y^2\left(a-b+c\right)+2xy\left(b-a-c\right)\)
\(=3x^2y^2\left(a-b+c\right)+2xy\left[-\left(a-b+c\right)\right]\)
\(=3x^2y^2\left(a-b+c\right)-2xy\left(a-b+c\right)\)
\(=\left(3x^2y^2-2xy\right)\left(a-b+c\right)\)
\(=xy\left(3xy-2\right)\left(a-b+c\right)\)
d, \(4x^2-4x+1\)\(=\left(2x\right)^2-2.2x.1+1^2\)\(=\left(2x-1\right)^2\)
j, \(16x^2+24xy+9y^2\)
\(=\left(4x\right)^2+2.4x.3y+\left(3y\right)^2\)
\(=\left(4x-3y\right)^2\)
g, \(x^2-64y^2\)\(=x^2-\left(8y\right)^2\)\(=\left(x-8y\right)\left(x+8y\right)\)