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c: =(x-2)(x-4)
b: \(=x\left(x^2+2xy+y^2-4\right)\)
=x(x+y-2)(x+y+2)
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\(a,x^2+6x=x\left(x+6\right)\\ b,9x^2-1=\left(3x\right)^2-1^2=\left(3x-1\right)\left(3x+1\right)\\ c,x^2+2xy-9+y^2=\left(x^2+2xy+y^2\right)-9=\left(x+y\right)^2-3^2=\left(x+y-3\right)\left(x+y+3\right)\\ c,x^2-y^2-x+y=\left(x-y\right)\left(x+y\right)-\left(x-y\right)=\left(x-y\right)\left(x+y-1\right)\)
a/ \(3x+6y-12xy\)
\(=3\left(x+2y-4xy\right)\)
b/ \(x^2-2x+xy-2y\)
\(=x\left(x-2\right)+y\left(x-2\right)\)
\(=\left(x-2\right)\left(x+y\right)\)
c/ \(5x^2-5z^2\)
\(=5\left(x^2-z^2\right)\)
\(=5\left(x-z\right)\left(x+z\right)\)
d/ \(x^2-9+2x\left(x-3\right)\)
\(=\left(x-3\right)\left(x+3\right)+2x\left(x+3\right)\)
\(=\left(x+3\right)\left(3x-3\right)\)
\(=3\left(x+3\right)\left(x-3\right)\)
\(a,x\left(x+6\right)\\ b,\left(9x-1\right)\left(9x+1\right)\\ c,\left(x+y\right)-3^2\\ =\left(x+y-3\right)\left(x+y+3\right)\\ d,\left(x-y\right)\left(x+y\right)-\left(x-y\right)\\ =\left(x-y\right)\left(x+y-1\right)\)
a: \(81x^5-x^3\)
\(=x^3\left(81x^2-1\right)\)
\(=x^3\left(9x-1\right)\left(9x+1\right)\)
b: \(9x^2y-12xy+4y\)
\(=y\left(9x^2-12x+4\right)\)
\(=y\left(3x-2\right)^2\)
c: \(\left(5-x\right)^2-16\left(x-2\right)^2\)
\(=\left(x-5\right)^2-\left(4x-8\right)^2\)
\(=\left(x-5-4x+8\right)\left(x-5+4x-8\right)\)
\(=-3\left(x-1\right)\left(5x-13\right)\)
d: Ta có: \(9x^2-y^2-21x-7y\)
\(=\left(3x-y\right)\left(3x+y\right)-7\left(3x+y\right)\)
\(=\left(3x+y\right)\left(3x-y-7\right)\)
e: Ta có: \(-y^2+8y-16+9x^2\)
\(=-\left(y^2-8y+16-9x^2\right)\)
\(=-\left(y-4-3x\right)\left(y-4+3x\right)\)
f: Ta có: \(5x^2-4x-1\)
\(=5x^2-5x+x-1\)
\(=5x\left(x-1\right)+\left(x-1\right)\)
\(=\left(x-1\right)\left(5x+1\right)\)
a) \(4x^2-1\)
\(=\left(2x\right)^2-1^2\)
\(=\left(2x-1\right)\left(2x+1\right)\)
b) \(x^2-3y^2\)
\(=x^2-\left(y\sqrt{3}\right)^2\)
\(=\left(x-y\sqrt{3}\right)\left(x+y\sqrt{3}\right)\)
c) \(9x^2-\dfrac{1}{4}\)
\(=\left(3x\right)^2-\left(\dfrac{1}{2}\right)^2\)
\(=\left(3x-\dfrac{1}{2}\right)\left(3x+\dfrac{1}{2}\right)\)
d) \(\left(x-y\right)^2-4\)
\(=\left(x-y\right)^2-2^2\)
\(=\left(x-y-2\right)\left(x-y+2\right)\)
e) \(9-\left(x-y\right)^2\)
\(=3^2-\left(x-y\right)^2\)
\(=\left(3+x-y\right)\left(3-x+y\right)\)
f) \(\left(x^2+4\right)^2-16x^2\)
\(=\left(x^2+4\right)^2-\left(4x\right)^2\)
\(=\left(x^2-4x+4\right)\left(x^2+4x+4\right)\)
\(=\left(x-2\right)^2\left(x+2\right)^2\)
a: \(=x^2\left(2x+3\right)+\left(2x+3\right)\)
\(=\left(2x+3\right)\left(x^2+1\right)\)
b: \(=\left(x-4\right)\left(x+3\right)\)
e: =(x+3)(x-2)
a) \(=x^2\left(2x+3\right)+\left(2x+3\right)=\left(2x+3\right)\left(x^2+1\right)\)
b) \(=x\left(x-4\right)+3\left(x-4\right)=\left(x-4\right)\left(x+3\right)\)
c) \(=\left(2x\right)^2-\left(x^2+1\right)^2=\left(x^2-2x+1\right)\left(x^2+2x+1\right)=\left(x-1\right)^2\left(x+1\right)^2\)
d) \(=4xy\left(y-3x+2\right)\)
e) \(=x\left(x-2\right)+3\left(x-2\right)=\left(x-2\right)\left(x+3\right)\)
f) \(=x\left(x^2+2xy+y^2-4z^2\right)=x\left[\left(x+y\right)^2-4z^2\right]=x\left(x+y-2z\right)\left(x+y+2z\right)\)
g) \(=x\left(x^2-2xy+y^2-25\right)=x\left[\left(x-y\right)^2-25\right]=x\left(x-y-5\right)\left(x-y+5\right)\)
h) \(=x\left(x+1\right)-3\left(x+1\right)=\left(x+1\right)\left(x-3\right)\)
i) \(=x^2\left(x-3\right)-9\left(x-3\right)=\left(x-3\right)\left(x^2-9\right)=\left(x-3\right)^2\left(x+3\right)\)
\(a,=\left(3x-11\right)\left(3x+11\right)\\ b,=\left(3x+1-x+2\right)\left(3x+1+x-2\right)\\ =\left(2x+3\right)\left(4x-1\right)\\ c,=\left(2x+1-8\right)\left(2x+1+8\right)=\left(2x-7\right)\left(2x+9\right)\)
\(9x^2-12xy-20y-25=9x^2-25-4y\left(3x+5\right)\)
\(=\left(3x+5\right)\left(3x-5\right)-4y\left(3x+5\right)=\left(3x+5\right)\left(3x-4y-5\right)\)
\(xy^2-49x^3-28x^2-4x=x\left[y^2-\left(49x^2+28x+4\right)\right]\)
\(=x\left[y^2-\left(7x+2\right)^2\right]=x\left(y+7x+2\right)\left(y-7x-2\right)\)
\(x^2-3x-2019.2022=x^2-3x-2019\left(2019+3\right)\)
\(=x^2-3x-2019^2-3.2019=\left(x-2019\right)\left(x+2019\right)-3\left(x+2019\right)\)
\(=\left(x+2019\right)\left(x-2022\right)\)
a: \(9x^2-12xy-20y-25\)
\(=\left(3x-5\right)\left(3x+5\right)-4y\left(3x+5\right)\)
\(=\left(3x+5\right)\left(3x-5-4y\right)\)