a/ 4x3 – xy2
b/ 5x3 – 10x2 + 5x
c/4x2 +24x+36-4y2
d/ 4x2y2 - 8xy2 + 4y2
e/ x3y + 10x2y + 35xy
f/2x3 –4x2y+2xy2–8x
g/3x2 –9xy–6x+18y
h/ x2y2 – 3xy2 + 2xy – 6y
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d) \(4x^2y^2-8xy^2+4y^2=4y^2\left(x^2-2x+1\right)=4y^2\left(x-1\right)^2\)
e) \(x^3y+10x^2y+35xy=xy\left(x^2+10x+35\right)\)
f) \(2x^3-4x^2y+2xy^2-8x=2x\left(x^2-2xy+y^2-4\right)=2x\left[\left(x-y\right)^2-4\right]=2x\left(x-y-2\right)\left(x-y+2\right)\)
g) \(3x^2-9xy-6x+18y=3x\left(x-3y\right)-6\left(x-3y\right)=3\left(x-3y\right)\left(x-2\right)\)
h) \(x^2y^2-3xy^2+2xy-6y=xy\left(xy+2\right)-3y\left(xy+2\right)=\left(xy+2\right)\left(xy-3y\right)=y\left(xy+2\right)\left(x-3\right)\)
d: \(4x^2y^2-8xy^2+4y^2\)
\(=4y^2\left(x^2-2x+1\right)\)
\(=4y^2\left(x-1\right)^2\)
e: \(x^3y+10x^2y+35xy\)
\(=xy\left(x^2+10x+35\right)\)
f: \(2x^3-4x^2y+2xy^2-8x\)
\(=2x\left(x^2-2xy+y^2-4\right)\)
\(=2x\left(x-y-2\right)\left(x-y+2\right)\)
e: \(x^2+6x+9-y^2\)
\(=\left(x+3\right)^2-y^2\)
\(=\left(x+3-y\right)\left(x+3+y\right)\)
f: \(x^2-2x+7x-14\)
\(=x\left(x-2\right)+7\left(x-2\right)\)
=(x-2)(x+7)
h: \(5x^2-10xy+5y^2-20\)
\(=5\left(x^2-2xy+y^2-4\right)\)
\(=5\left(x-y-2\right)\left(x-y+2\right)\)
a: \(3x^4-6x^3+2x^2=x^2\left(3x^2-6x+2\right)\)
b: \(x^3y+12x^2y+36xy=xy\left(x^2+12x+36\right)=xy\left(x+6\right)^2\)
c: \(x^3y-9xy^3=xy\left(x^2-9y^2\right)=xy\left(x-3y\right)\left(x+3y\right)\)
d: \(x^2y^2-2xy^2+y^2=y^2\left(x-1\right)^2\)
1) x³ + 2x² + x
= x(x² + 2x + 1)
= x(x + 1)²
2) 5x³ - 10x² + 5x
= 5x(x² - 2x + 1)
= 5x(x - 1)²
3) 8x²y - 8xy + 2x
= 2x(4xy - 4y + 1)
5) 2x² + 5x³ + x²y
= x²(2 + 5x + y)
6) 4x²y - 8xy² + 18x²y²
= 2xy(2x - 4y + 9xy)
\(a.x\left(2x+5\right)=2x^2+5x\)
\(b.3x^2\left(5x^3-2x+9\right)=15x^5-6x^3+27x^2\)
\(c.\left(x+2\right)\left(4x^3+x-7\right)=4x^4+x^2-7x+8x^3+2x-14=4x^4+8x^3+x^2-5x-14\)
\(d.\left(16x^2+12x^3y^4-4x^2y\right):4x^2y=4x^3+3x^2y^3-1\)
\(A+B=7x^2-3xy+2y^2\)
\(A-B=x^2-7xy+4y^2\)
Bài 2
\(C+D=-x^2y+4xy+6x-3\)
\(C-D=9x^2y-14xy+19\)
a: \(4x^3-xy^2\)
\(=x\left(4x^2-y^2\right)\)
\(=x\left(2x-y\right)\left(2x+y\right)\)
b: \(5x^3-10x^2+5x\)
\(=5x\left(x^2-2x+1\right)\)
\(=5x\left(x-1\right)^2\)
c: \(4x^2+24x+36-4y^2\)
\(=4\left(x^2+6x+9-y^2\right)\)
\(=4\left(x+3-y\right)\left(x+3+y\right)\)
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