x^2+2x-9x^2+1
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\(=\left(x^2+2x\right)^2+9\left(x^2+2x\right)+20\)
\(=\left(x^2+2x+4\right)\left(x^2+2x+5\right)\)
\(\Rightarrow\left(x^2+2x\right)^2+9\left(x^2+2x\right)+20=\left(x^2+2x\right)^2+4\left(x^2+2x\right)+5\cdot\left(x^2+2x\right)+20=\left(x^2+2x\right)\left(x^2+2x+4\right)+5\left(x^2+2x+4\right)=\left(x^2+2x+4\right)\left(x^2+2x+5\right)\)
\(=x^3+2x^2-8x=x\left(x^2+2x-8\right)\\ =x\left(x^2-2x+4x-8\right)\\ =x\left(x-2\right)\left(x+4\right)\)
\(\left(x^2+2x\right)^2+4\left(x^2+2x\right)+5\left(x^2+2x\right)+20\)
\(=\left(x^2+2x\right)\left(x^2+2x+4\right)+5\left(x^2+2x+4\right)\)
\(=\left(x^2+2x+5\right)\left(x^2+2x+4\right)\)
x3 + 2x2y + xy2 - 9x
= x( x2 + 2xy + y2 - 9 )
= x[ ( x2 + 2xy + y2 ) - 9 ]
= x[ ( x + y )2 - 32 ]
= x( x + y - 3 )( x + y + 3 )
Bài làm
\(x^3+2x^2y+xy^2-9x=x\left(x^2+2xy+y^2-9\right)\)
\(=x\left[\left(x+y\right)^2-9\right]=x\left(x+y-3\right)\left(x+y+3\right)\)
\(4x^2-4xy+y^2\)
\(=\left(2x\right)^2-2\cdot2x\cdot y+y^2\)
\(=\left(2x-y\right)^2\)
\(---\)
\(\left(x+1\right)^2-9y^2\)
\(=\left(x+1\right)^2-\left(3y\right)^2\)
\(=\left(x+1-3y\right)\left(x+1+3y\right)\)
\(=\left(x-3y+1\right)\left(x+3y+1\right)\)
\(---\)
\(2x+5^2-9x^2\) (kt lại đề bài)
\(2x-1^2-3x-1^2\)
\(=-x-2=-1\cdot\left(x+2\right)\)
x2 + 2x - 9x2 + 1
= - 8x2 + 2x + 1
= - 8x2 + 4x - 2x + 1
= - 8x \(\left(x-\frac{1}{2}\right)\) - 2 \(\left(x-\frac{1}{2}\right)\)
= \(\left(x-\frac{1}{2}\right)\left(-8x-2\right)\)
= \(-2\left(x-\frac{1}{2}\right)\left(4x+1\right)\)
\(x^2-2x-9x^2+1\)
=\(\left(x^2-2x+1\right)-9x^2\)
=\(\left(x-1\right)^2-\left(3x\right)^2\)
=\(\left(x-1+3x\right)\left(x-1-3x\right)\)
=\(\left(4x-1\right)\left(-2x-1\right)\)