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a) \(A=x^2-2xy+y^2+3x-3y-4\)
\(=\left(x-y\right)^2-1+3x-3y-3\)
\(=\left(x-y-1\right)\left(x-y+1\right)+3\left(x-y-1\right)\)
\(=\left(x-y-1\right)\left(x-y+1+3\right)\)
\(=\left(x-y-1\right)\left(x-y+4\right)\)
3*(\(4x^2-4xy+y^2\))-10(2x-y)+8
3*(2x-y)^2-10(2x-y)+8
3*(2x-y)^2-6(2x-y)-4(2x-y)+8
3(2x-y)(2x-y-2)-4(2x-y-2)
(2x-y-2)(6x-3y-40
\(\left(12x^2-12xy+3y^2\right)-10\left(2x-y\right)+8\)
\(=\left(12x^2-6xy-6xy+3y^2\right)-10\left(2x-y\right)+8\)
\(=\left[6x\left(2x-y\right)-3y\left(2x-y\right)\right]-10\left(2x-y\right)+8\)
\(=\left(2x-y\right)\left(6x-3y\right)-10\left(2x-y\right)+8\)
\(=3\left(2x-y\right)^2-10\left(2x-y\right)+8\)
Đặt \(2x-y=a\), khi đó biểu thức có dạng:
\(3a^2-10a+8=3a^2-6a-4a+8\)
\(=3a\left(a-2\right)-4\left(a-2\right)=\left(a-2\right)\left(3a-4\right)\)
\(=\left(2x-y-2\right)\left(6x-3y-4\right).\)
a.
\(5x^2\left(x-2y\right)-15x\left(x-2y\right)\)
\(=\left(x-2y\right)\left(5x^2-15x\right)\)
\(=5x\left(x-2y\right)\left(x-3\right)\)
b.
\(3\left(x-y\right)-5x\left(y-x\right)\)
\(=3\left(x-y\right)+5x\left(x-y\right)\)
\(=\left(x-y\right)\left(3+5x\right)\)
\(a.\) \(ax^2-a^2x-x+a\)
\(=\left(ax^2-a^2x\right)-\left(x-a\right)\)
\(=ax\left(x-a\right)-\left(x-a\right)\)
\(=\left(ax-1\right)\left(x-a\right)\)
\(b.\) \(18x^3-12x^2+2x\)
\(=2x\left(9x^2-6x+1\right)\)
\(=2x\left(3x-1\right)^2\)
\(c.\) \(x^3-5x^2-4x+20\)
\(=\left(x^3-5x^2\right)-\left(4x-20\right)\)
\(=x^2\left(x-5\right)-4\left(x-5\right)\)
\(=\left(x^2-4\right)\left(x-5\right)\)
\(=\left(x-2\right)\left(x+2\right)\left(x-5\right)\)
\(d.\) \(\left(x+7\right)\left(x+15\right)+15\)
\(=x^2+15x+7x+105+15\)
\(=x^2+22x+120\)
\(=\left(x+10\right)\left(x+12\right)\)
a: \(=\left(x+2\right)\left(x+3\right)\left(x-7\right)\left(x-8\right)-144\)
\(=\left(x^2-5x-14\right)\left(x^2-5x-24\right)-144\)
\(=\left(x^2-5x\right)^2-38\left(x^2-5x\right)+192\)
\(=\left(x^2-5x\right)^2-32\left(x^2-5x\right)-6\left(x^2-5x\right)+192\)
\(=\left(x^2-5x-32\right)\left(x^2-5x-6\right)\)
\(=\left(x^2-5x-32\right)\left(x-6\right)\left(x+1\right)\)
b: \(=\left(12x^2-12xy+3y^2\right)-20x+10y+8\)
\(=\left[3\left(2x-y\right)^2\right]-10\left(2x-y\right)+8\)
\(=3\left(2x-y\right)^2-4\left(2x-y\right)-6\left(2x-y\right)+8\)
\(=\left(2x-y\right)\left(6x-3y-4\right)-2\left(6x-3y-4\right)\)
\(=\left(6x-3y-4\right)\left(2x-y-2\right)\)