a: \(=\dfrac{2xy\left(2x^2y-4x+5\right)}{2xy}=2x^2y-4x+5\)

b: \(=\dfrac{x^2y\left(7x^2y-2y-5x^2y^3\right)}{3x^2y}=\dfrac{7}{3}x^2y-\dfrac{2}{3}y-\dfrac{5}{3}x^2y^3\)

8x³-(2x+y).(4x²-2xy+y²)

=\(\left(2x\right)^3-\left(2x+y\right).\left[\left(2x\right)^2-2x.y+y^2\right]\)

= \(\left(2x\right)^3-\left[\left(2x\right)^3+y^3\right]\)

= \(\left(2x\right)^3-\left(2x\right)^3-y^3\)

= -y³

^{Học tốt !}

\(8x^3-\left(2x+y\right)\left(4x^2-2xy+y^2\right)\)

\(=8x^3-8x^3-y^3\)

\(=-y^3\)

lớp 12 bạn

\(Bài1:\\ a,\left(4x-1\right)\left(2x^2-x-1\right)=4x\left(2x^2-x-1\right)-\left(2x^2-x-1\right)=8x^3-4x^2-4x-2x^2+x+1=8x^3-6x^2-3x+1\\ b,\left(4x^3+8x^2-2x\right):2x\\ =2x\left(2x^2+4x-1\right):2x\\ =2x^2+4x-1\)

\(Bài2:\\ a,2x^3-8x^2+8x=2x\left(x^2-4x+4\right)=2x\left(x-2\right)^2\\ b,2xy+2x+yz+z=2x\left(y+1\right)+z\left(y+1\right)=\left(y+1\right)\left(2x+z\right)\\ c,x^2+2x+1-y^2=\left(x+1\right)^2-y^2=\left(x-y+1\right)\left(x+y+1\right)\)

ukm thiếu ý c bài 1 nha bn XD

Bài 3:

A(x)⋮B(x)

=>\(3x^2+5x+m\) ⋮x-2

=>\(3x^2-6x+11x-22+m+22\) ⋮x-2

=>m+22=0

=>m=-22

Bài 2:

a: \(2x^3-8x^2+8x\)

\(=2x\left(x^2-4x+4\right)\)

\(=2x\left(x-2\right)^2\)

b: 2xy+2x+yz+z

=2x(y+1)+z(y+1)

=(y+1)(2x+z)

c: \(x^2+2x+1-y^2\)

\(=\left(x+1\right)^2-y^2\)

=(x+1-y)(x+1+y)

Câu 1:

a:\(\left(4x-1\right)\left(2x^2-x-1\right)\)

\(=8x^3-4x^2-4x-2x^2+x+1\)

\(=8x^3-6x^2-3x+1\)

b: \(\left(4x^3+8x^2-2x\right):2x\)

\(=\frac{4x^3}{2x}+\frac{8x^2}{2x}-\frac{2x}{2x}\)

\(=2x^2+4x-1\)

c: \(\left(6x^3-7x^2-16x+12\right):\left(2x+3\right)\)

\(=\left(6x^3+9x^2-16x^2-24x+8x+12\right):\left(2x+3\right)\)

\(=\left\lbrack3x^2\left(2x+3\right)-8x\left(2x+3\right)+4\left(2x+3\right)\right\rbrack:\left(2x+3\right)\)

\(=3x^2-8x+4\)

\(\dfrac{8x^3+y^3}{y^3+2xy^2+y^2-4x^2}\\ =\dfrac{\left(2x+y\right)\left(4x^2-2xy+y^2\right)}{\left(y^3+2xy^2\right)+\left(y^2-4x^2\right)}\\ =\dfrac{\left(2x+y\right)\left(4x^2-2xy+y^2\right)}{y^2\left(y+2x\right)+\left(y-2x\right)\left(y+2x\right)}\\ =\dfrac{\left(y+2x\right)\left(4x^2-2xy+y^2\right)}{\left(y+2x\right)\left(y^2+y-2x\right)}\\ =\dfrac{4x^2-2xy+y^2}{y^2+y-2x}\)

\(\dfrac{8x^3+y^3}{y^3+2xy^2+y^2-4x^2}\)

\(=\dfrac{\left(2x+y\right)\left(4x^2-2xy+y^2\right)}{y^2\left(y+2x\right)+\left(y+2x\right)\left(y-2x\right)}\)

\(=\dfrac{4x^2-2xy+y^2}{y^2+y-2x}\)

a, \(=12x^5+9x^3y^2-6x^2y^3-20x^4y-15x^2y^3-10xy^4-24x^3y^2-18xy^4+12y^5\)

(tự rút gọn cái :P)

b, \(8x^3+4x^2y-2xy^2-y^3\)

\(=4x^2\left(2x+y\right)-y^2\left(2x+y\right)=\left(2x+y\right)^2\left(2x-y\right)\)

\(4x^2y^2-4x^2-4xy-y^2=4x^2y^2-\left(2x+y\right)^2\)

\(=\left(2x+y+2xy\right)\left(2xy-2x+y\right)\)

Mấy cái còn lại nhân tung ra là được mà :))))

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