Phân tích đa thức thành nhân tử:
a) 25 y 2 + 10 y 8 +1;
b) ( x - 1 ) 4 - 2 ( x 2 - 2 x + 1 ) 2 +1;
c) (x + 1)(x + 2)(x + 3)(x + 4) - 24;
d) ( x 2 + 4 x + 8 ) 2 + 3 x ( x 2 + 4x + 8) + 2 x 2 ;
e) x 4 + 6 x 3 +7 x 2 -6x + 1.
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a) \(45x\left(y-8\right)-27x\left(8-y\right)=45x\left(y-8\right)+27x\left(y-8\right)=\left(y-8\right)\left(45x+27x\right)=72x\left(y-8\right)\)
b) \(x^2-49+4y^2-4xy=\left(x-2y\right)^2-7^2=\left(x-2y-7\right)\left(x-2y+7\right)\)
a,=x(y-8)(45+27)=x(y-8)72
\(b,=\left(x-2y\right)^2-49=\left(x-2y+7\right)\left(x-2y-7\right)\)
tick mik nha
\(a,=2xy\left(2y-x\right)\\ b,=x^2\left(x-4\right)+5\left(x-4\right)=\left(x^2+5\right)\left(x-4\right)\\ c,=\left(x-y\right)\left(x^2-25\right)=\left(x-y\right)\left(x-5\right)\left(x+5\right)\)
\(a,=x\left(x^2-4x+4-z^2\right)=x\left[\left(x-2\right)^2-z^2\right]=x\left(x-z-2\right)\left(x+z-2\right)\\ b,=\left(x-y\right)^2-\left(z-5\right)^2=\left(x-y-z+5\right)\left(x-y+z-5\right)\)
\(x^3-4x^2+4x-xz^2=x\left(x^2-4x+4-z^2\right)\)
\(=x\left[\left(x-2\right)^2-z^2\right]=x\left(x-2-z\right)\left(x-2+z\right)\)
\(x^2-2xy+y^2-z^2+10z-25\)
\(=\left(x-y\right)^2-\left(z-5\right)^2\)
\(=\left(x-y+z-5\right)\left(x-y-z+5\right)\)
`a, 8x^3 - 1 = (2x-1)(4x^2 + 2x - 1)`
`b, x^3 + 27y^3 = (x+3y)(x^3 - 3xy + 9y^2)`
`c, x^3 - y^6 = (x-y^2)(x+xy^2 + y^4)`
1A:
a: \(x^3+2x=x\left(x^2+2\right)\)
b: \(3x-6y=3\left(x-2y\right)\)
c: \(5\left(x+3y\right)-15x\left(x+3y\right)\)
\(=5\left(x+3y\right)\left(1-3x\right)\)
d: \(3\left(x-y\right)-5x\left(y-x\right)\)
\(=3\left(x-y\right)+5x\left(x-y\right)\)
\(=\left(x-y\right)\left(5x+3\right)\)
1A. a. x(x2+2)
b. 3(x-2y)
c. 5(x+3y)(1-3x)
d. (x-y) (3-5x)
1B. a. 2x(2x-3)
b.xy(x2-2xy+5)
c. 2x(x+1)(x+2)
d. 2x(y-1)+2y(y-1)=2(y-1)(x-y)
\(a,2x\left(x-3\right)\\ b,x^2-\left(y+1\right)^2\\ =\left(x-y-1\right)\left(x+y+1\right)\)
c: \(x^2-10x+21=\left(x-3\right)\left(x-7\right)\)
a: \(x^2y+xy^3-xy-y^3\)
\(=xy\left(x-1\right)+y^3\left(x-1\right)\)
\(=y\left(x-1\right)\left(x+y^2\right)\)
\(a) x^2y+xy^3-xy-y^3\\=(x^2y+xy^3)-(xy+y^3)\\=xy(x+y^2)-y(x+y^2)\\=(x+y^2)(xy-y)\\=y(x+y^2)(x-1)\\b)2x^2+5x+8(xem lại đề)\\c)x^2-10x+21\\=x^2-3x-7x+21\\=x(x-3)-7(x-3)\\=(x-3)(x-7)\)
\(a,=xy\left(x+y^2\right)-y\left(x+y^2\right)=y\left(x+y^2\right)\left(x-1\right)\\ c,=x^2-7x-3x+21=\left(x-7\right)\left(x-3\right)\)
a: \(=\dfrac{2}{5}\left(xy-x-y^2+1\right)\)
\(=\dfrac{2}{5}\left[x\left(y-1\right)-\left(y-1\right)\left(y+1\right)\right]\)
\(=\dfrac{2}{5}\left(y-1\right)\left(x-y-1\right)\)
b: \(=x\left(x^2+2xy+y^2-9\right)\)
\(=x\left(x+y-3\right)\left(x+y+3\right)\)
a) =25(xy−x−y2+1)=25(xy−x−y2+1)
=25[x(y−1)−(y−1)(y+1)]=25[x(y−1)−(y−1)(y+1)]
=25(y−1)(x−y−1)=25(y−1)(x−y−1)
b) =x(x2+2xy+y2−9)=x(x2+2xy+y2−9)
=x(x+y−3)(x+y+3)