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a) Xem lại đề
b) x³ - 4x²y + 4xy² - 9x
= x(x² - 4xy + 4y² - 9)
= x[(x² - 4xy + 4y² - 3²]
= x[(x - 2y)² - 3²]
= x(x - 2y - 3)(x - 2y + 3)
c) x³ - y³ + x - y
= (x³ - y³) + (x - y)
= (x - y)(x² + xy + y²) + (x - y)
= (x - y)(x² + xy + y² + 1)
d) 4x² - 4xy + 2x - y + y²
= (4x² - 4xy + y²) + (2x - y)
= (2x - y)² + (2x - y)
= (2x - y)(2x - y + 1)
e) 9x² - 3x + 2y - 4y²
= (9x² - 4y²) - (3x - 2y)
= (3x - 2y)(3x + 2y) - (3x - 2y)
= (3x - 2y)(3x + 2y - 1)
f) 3x² - 6xy + 3y² - 5x + 5y
= (3x² - 6xy + 3y²) - (5x - 5y)
= 3(x² - 2xy + y²) - 5(x - y)
= 3(x - y)² - 5(x - y)
= (x - y)[(3(x - y) - 5]
= (x - y)(3x - 3y - 5)
\(a,x^2-y^2-2x+2y=\left(x^2-y^2\right)-\left(2x-2y\right)=\left(x-y\right)\left(x+y\right)-2\left(x-y\right)=\left(x-y\right)\left(x+y-2\right).\) \(b,2x+2y-x^2-xy=2\left(x+y\right)-x\left(x+y\right)=\left(x+y\right)\left(2-x\right)\)
\(c,3a^2-6ab+3b^2-12c^2=3\left(a^2-2ab+b^2-4c^2\right)=3.\left(\left(a-b\right)^2-\left(2c\right)^2\right)\)
\(=3\left(a-b-2c\right).\left(a-b+2c\right)\)
\(d,x^2-25+y^2-2xy=\left(x^2-2xy+y^2\right)-5^2=\left(x-y\right)^2-5^2\)
\(=\left(x-y+5\right)\left(x-y-5\right)\)
\(e,a^2+2ab+b^2-ac-bc=\left(a+b\right)^2-c\left(a+b\right)=\left(a+b\right)\left(a+b-c\right)\)
\(f,x^2-2x-4y^2-4y=\left(x^2-4y^2\right)-\left(2x+4y\right)=\left(x-2y\right)\left(x+2y\right)-2\left(x+2y\right)\)
\(=\left(x+2y\right)\left(x-2y-2\right)\)
\(h,x^2\left(x-1\right)+16\left(1-x\right)=x^2\left(x-1\right)-16\left(x-1\right)=\left(x-1\right)\left(x^2-16\right)=\)
\(=\left(x-1\right)\left(x-4\right)\left(x+4\right)\)
\(x^2-y^2-2x+2y=\left(x+y\right)\left(x-y\right)-2\left(x-y\right)=\left(x+y-2\right)\left(x-y\right)\) \(2x+2y-x^2-xy=2\left(x+y\right)-x\left(x+y\right)=\left(2-x\right)\left(x+y\right)\)
\(3a^2-6ab+3b^2-12c^2=3\left(a^2-2ab+b^2-4c^2\right)=3\left(a-b\right)^2-3\left(2c\right)^2=3\left(a-b+2c\right)\left(a-b-2c\right)\) \(x^2-25+y^2+2xy=\left(x+y\right)^2-25=\left(x+y-5\right)\left(x+y+5\right)\)
\(a^2+2ab+b^2-ac-bc=\left(a+b\right)^2-c\left(a+b\right)=\left(a+b\right)\left(a+b-c\right)\)
\(x^2-2x+1-4y^2-4y-1=\left(x-1\right)^2-\left(2y+1\right)^2=\left(x+2y\right)\left(x-2y-2\right)\)\(x^2\left(x-1\right)-16\left(x-1\right)=\left(x-1\right)\left(x^2-16\right)=\left(x-1\right)\left(x+4\right)\left(x-4\right)\) \(x^2y-x^3-9y+9x=x^2\left(y-x\right)-9\left(y-x\right)=\left(y-x\right)\left(x^2-9\right)\left(y-x\right)\left(x-3\right)\left(x+3\right)\)
i. Ta có: (x+y)^3 - (x-y)^3=[(x+y)-(x-y)][(x+y)^2 + (x+y)(x-y) + (x-y)^2]
=2y(x^2 +2xy +y^2 +x^2 -xy +xy -y^2 +x^2 -2xy +y^2)
=2y(3x^2 +y^2)
a: Ta có: \(\left(8x^3-4x^2\right):4x-\left(4x^2-5x\right):2x+\left(2x\right)^2\)
\(=2x^2-x-2x+\dfrac{5}{2}+4x^2\)
\(=6x^2-3x+\dfrac{5}{2}\)
b: Ta có: \(\left(3x^3-x^2y\right):x^2-\left(xy^2+x^2y\right):xy+2x\left(x-1\right)\)
\(=3x-y-y-x+2x^2-2x\)
\(=2x^2-2y\)
a) 2x^2 - 2xy - 5x +5y
= (2x^2 - 2xy ) - ( 5x- 5 y)
=2x(x-y) - 5(x-y)
=(x- y). (2x- 5)
b)8x2 +4xy-2ax-ay
=(8x2 +4xy) -(2ax+ay)
=4x(2x+y)-a(2x+y)
=(2x+y).(4x-a)
c)=x(x2 -4x +4)
=x(x-2)2
d)=16- (x2 -2xy +y^2)
=4^2-(x-y)^2
=(4-x+y).(4+x-y)
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