Thực hiện các phép tính sau
a) M = ( 2x3y ) . ( x2 - 2y + 1 )
b) ( x + y ) . ( x2y - x )
c) N = ( 2xy3 - 4y - 8x ) . ( \(\dfrac{1}{2}\)y )
d) ( x + 2y ) . ( x2 - 2y + 4z)
e) 8x6y7z2 : 4x4y7
f) 65x9y5 : ( -13x4y4 )
g) ( x3 + 12x2 - 5x ) : x
h) ( 3x4y3 - 9x2y2 + 15xy3 ) : xy2
i) ( x + 1 )2
k) ( 2x - 1 )2
l) ( x - 3 ) . ( 3 + x )
m) ( x2 + 2 )2
K cần lm hết, bt câu nào thì chỉ. Gấc cẻm ưn :)
a: \(M=\left(2x^3y\right)\left(x^2-2y+1\right)\)
\(=2x^3y\cdot x^2-2x^3y\cdot2y+2x^3y\cdot1\)
\(=2x^5y-4x^3y^2+2x^3y\)
b: \(\left(x+y\right)\left(x^2y-x\right)\)
\(=x\cdot x^2y-x\cdot x+y\cdot x^2y-y\cdot x\)
\(=x^3y-x^2+x^2y^2-xy\)
c: \(N=\left(2xy^3-4y-8x\right)\cdot\left(\dfrac{1}{2}y\right)\)
\(=2xy^3\cdot\dfrac{1}{2}y-4y\cdot\dfrac{1}{2}y-8x\cdot\dfrac{1}{2}y\)
\(=xy^4-2y^2-4xy\)
d: \(\left(x+2y\right)\left(x^2-2y+4z\right)\)
\(=x\cdot x^2-x\cdot2y+x\cdot4z+2y\cdot x^2-2y\cdot2y+2y\cdot4z\)
\(=x^3-2xy+4xz+2x^2y-4y^2+8yz\)
e: \(8x^6y^7z^2:4x^4y^7\)
\(=\left(\dfrac{8}{4}\right)\cdot\left(\dfrac{x^6}{x^4}\right)\cdot\dfrac{y^7}{y^7}\cdot z^2\)
\(=2x^2z^2\)
f: \(65x^9y^5:\left(-13x^4y^4\right)\)
\(=-\dfrac{65}{13}\cdot\dfrac{x^9}{x^4}\cdot\dfrac{y^5}{y^4}\)
\(=-5x^5y\)
g: \(\dfrac{x^3+12x^2-5x}{x}\)
\(=\dfrac{x\left(x^2+12x-5\right)}{x}=x^2+12x-5\)
h: \(\dfrac{3x^4y^3-9x^2y^2+15xy^3}{xy^2}\)
\(=\dfrac{3x^4y^3}{xy^2}-\dfrac{9x^2y^2}{xy^2}+\dfrac{15xy^3}{xy^2}\)
\(=3x^3y-9x+15y\)
i: \(\left(x+1\right)^2=x^2+2\cdot x\cdot1+1^2=x^2+2x+1\)
k: \(\left(2x-1\right)^2=\left(2x\right)^2-2\cdot2x\cdot1+1^2=4x^2-4x+1\)
l: \(\left(x-3\right)\left(x+3\right)=x^2-3^2=x^2-9\)
m: \(\left(x^2+2\right)^2\)
\(=\left(x^2\right)^2+2\cdot x^2\cdot2+2^2\)
\(=x^4+4x^2+4\)
a: \(M=\left(2x^3y\right)\left(x^2-2y+1\right)\)
\(=2x^3y\cdot x^2-2x^3y\cdot2y+2x^3y\cdot1\)
\(=2x^5y-4x^3y^2+2x^3y\)
b: \(\left(x+y\right)\left(x^2y-x\right)\)
\(=x\cdot x^2y-x\cdot x+y\cdot x^2y-y\cdot x\)
\(=x^3y-x^2+x^2y^2-xy\)
c: \(N=\left(2xy^3-4y-8x\right)\cdot\left(\dfrac{1}{2}y\right)\)
\(=2xy^3\cdot\dfrac{1}{2}y-4y\cdot\dfrac{1}{2}y-8x\cdot\dfrac{1}{2}y\)
\(=xy^4-2y^2-4xy\)
d: \(\left(x+2y\right)\left(x^2-2y+4z\right)\)
\(=x\cdot x^2-x\cdot2y+x\cdot4z+2y\cdot x^2-2y\cdot2y+2y\cdot4z\)
\(=x^3-2xy+4xz+2x^2y-4y^2+8yz\)
e: \(8x^6y^7z^2:4x^4y^7\)
\(=\left(\dfrac{8}{4}\right)\cdot\left(\dfrac{x^6}{x^4}\right)\cdot\dfrac{y^7}{y^7}\cdot z^2\)
\(=2x^2z^2\)
f: \(65x^9y^5:\left(-13x^4y^4\right)\)
\(=-\dfrac{65}{13}\cdot\dfrac{x^9}{x^4}\cdot\dfrac{y^5}{y^4}\)
\(=-5x^5y\)
g: \(\dfrac{x^3+12x^2-5x}{x}\)
\(=\dfrac{x\left(x^2+12x-5\right)}{x}=x^2+12x-5\)
h: \(\dfrac{3x^4y^3-9x^2y^2+15xy^3}{xy^2}\)
\(=\dfrac{3x^4y^3}{xy^2}-\dfrac{9x^2y^2}{xy^2}+\dfrac{15xy^3}{xy^2}\)
\(=3x^3y-9x+15y\)
i: \(\left(x+1\right)^2=x^2+2\cdot x\cdot1+1^2=x^2+2x+1\)
k: \(\left(2x-1\right)^2=\left(2x\right)^2-2\cdot2x\cdot1+1^2=4x^2-4x+1\)
l: \(\left(x-3\right)\left(x+3\right)=x^2-3^2=x^2-9\)
m: \(\left(x^2+2\right)^2\)
\(=\left(x^2\right)^2+2\cdot x^2\cdot2+2^2\)
\(=x^4+4x^2+4\)
