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\(16x^3y+\frac{1}{4}yz^3\)
\(\text{Phân tích thành nhân tử}\)
\(\frac{y\left(\frac{z}{2}+2x\right)\left(z^2-4xz+16x^2\right)}{2}\)
\(16x^3y+0,25yz^3=16x^3y+\frac{1}{4}yz^3\)
\(=\frac{1}{4}y\left(64x^3+z^3\right)=\frac{y}{4}\left(4x+z\right)\left(16x^2-4xz+z^2\right)\)
1) \(\left(3x^2-3y^2\right)-\left(12x-12y\right)\)
\(=3xy\left(x-y\right)-12\left(x-y\right)\)
\(=\left(3xy-12\right)\left(x-y\right)\)
2) \(4x^3+4xy^2+8x^2y-16x\)
\(=\left(4x^3-16x\right)+\left(4xy^2+8x^2y\right)\)
\(=4x\left(x^2-4\right)+4xy\left(y+2x\right)\)
Ta có : 3x2 - 3y2 - 12x + 12y
= (3x2 - 3y2) - (12x - 12y)
= 3(x2 - y2) - 12(x - y)
= 3(x - y)(x + y) - 4.3.(x - y)
= 3(x - y)(x + y - 4)
c, \(x^6-x^4+2x^3+2x^2\)
\(=x^2\left(x^4-x^2+2x+2\right)\)
\(=x^2[x^2\left(x-1\right)\left(x+1\right)+2\left(x+1\right)]\)
\(=x^2\left(x+1\right)\left(x^3-x^2+2\right)\)
\(=x^2\left(x+1\right)[x^2\left(x+1\right)-2x\left(x+1\right)+2\left(x+1\right)]\)
\(=x^2\left(x+1\right)^2\left(x^2-2x+2\right)\)
d,
\(2x^3-x^2-1\)
\(=2x^3-2x^2+x^2-x+x-1\)
\(=2x^2\left(x-1\right)+x\left(x-1\right)+\left(x-1\right)\)
\(=\left(x-1\right)\left(2x^2+x+1\right)\)
\(16x^4+8x^2+1-8x^2\)
\(=\left(4x^2+1\right)^2-8x^2\)
\(=\left(4x^2+1-x\sqrt{8}\right)\left(4x^2+1+x\sqrt{8}\right)\)
\(16x^4+y^4+4x^2y^2\)
\(=\left(4x^2\right)^2+2.4x^2.y^2+\left(y^2\right)^2-4x^2y^2\)
\(=\left(4x^2+y^2\right)-\left(2xy\right)^2\)
\(=\left(4x^2-2xy+y^2\right)\left(4x^2+2xy+y^2\right)\)
\(x^3-2x-4\)
\(=x^3-2x^2+2x^2-4x+2x-4\)
\(=x^2\left(x-2\right)+2x\left(x-2\right)+2\left(x-2\right)\)
\(=\left(x-2\right)\left(x^2+2x+2\right)\)
\(x^3+x^2+4\)
\(=x^3+2x^2-x^2-2x+2x+4\)
\(=x^2\left(x+2\right)-x\left(x+2\right)+2\left(x+2\right)\)
\(=\left(x+2\right)\left(x^2-x+2\right)\)
\(x^4+2x^3-16x^2-2x+15\)
\(=x^4+5x^3-3x^3-15x^2-x^2-5x+3x+15\)
\(=x^3\left(x+5\right)-3x^2\left(x+5\right)-x\left(x+5\right)+3\left(x+5\right)\)
\(=\left(x+5\right)\left(x^3-3x^2-x+3\right)\)
\(=\left(x+5\right)\left[x^2\left(x-3\right)-\left(x-3\right)\right]\)
\(=\left(x+5\right)\left(x-3\right)\left(x^2-1\right)\)
\(=\left(x-1\right)\left(x+1\right)\left(x-3\right)\left(x+5\right)\)
\(x^4-4x^3+8x^2-16x+16 \)
\(=x^3\left(x-2\right)-2x^2\left(x-2\right)+4x\left(x-2\right)-8\left(x-2\right)\)
\(=\left(x-2\right)\left(x^3-2x^2+4x-8\right)\)
\(=\left(x-2\right)\left[x^2\left(x-2\right)+4\left(x-2\right)\right]\)
\(=\left(x-2\right)^2\left(x^2+4\right)\)
Mình mới học lớp 5 à . Làm sao mk biết được.
\(16x^3y+\frac{1}{4}yz^3=\frac{1}{4}y\left(64x^3+z^3\right)=\frac{1}{4}y\left(4x+z\right)\left(16x^2-4xz+z^2\right)\)