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a) \(x^2y\left(5xy-2x^2y-y^2\right)\)
\(=5x^3y^2-2x^4y^2-x^2y^3\)
b) \(\left(x-2y\right)\left(2x^3+4xy\right)\)
\(=2x^4+4x^2y-4x^3y-8xy^2\)
b: Ta có: \(\left(4x-y\right)\left(4x+y\right)-2\left(3x-2y\right)^2+\left(x-3y\right)^2\)
\(=16x^2-y^2-2\left(9x^2-12xy+4y^2\right)+x^2-6xy+9y^2\)
\(=17x^2-6xy+8y^2-18x^2+24xy-8y^2\)
\(=-x^2+18xy\)
c: Ta có: \(\left(2a-3b+4c\right)\left(2a-3b-4c\right)\)
\(=\left(2a-3b\right)^2-16c^2\)
\(=4a^2-12ab+9b^2-16c^2\)
`a, (4-x)(4+x) = 16 - x^2`
`b, (2y+7z)(2y-7z) = 4y^2 - 49z^2`
`c, (x+2y^2)(x-2y^2)`
`= x^2 - 4y^4`
a) \(\left(-5a^4\right)\cdot\left(a^2b-ab^2\right)\)
\(=\left(-5a^4\cdot a^2b\right)-\left(-5a^4\cdot ab^2\right)\)
\(=-5a^6b+5a^5b^2\)
b) \(\left(x+2y\right)\left(xy^2-2y^3\right)\)
\(=x^2y^2-2xy^3+2xy^3-4y^4\)
\(=x^2y^2-4y^4\)
`a, (-5a^4)(a^2b - ab^2)`
`= -5(a^(4+2) . b) + 5a^(4+1) . b^2`
`= -5a^6b + 5a^5b^2`
`b, (x+2y)(xy^2-2y^3)`
`= x^2y^2 + 2xy^3 - 2xy^3 - 4y^4`
Bài 2:
1: \(\left(2x-1\right)^2-4\left(2x-1\right)=0\)
=>\(\left(2x-1\right)\left(2x-1-4\right)=0\)
=>(2x-1)(2x-5)=0
=>\(\left[{}\begin{matrix}2x-1=0\\2x-5=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1}{2}\\x=\dfrac{5}{2}\end{matrix}\right.\)
2: \(9x^3-x=0\)
=>\(x\left(9x^2-1\right)=0\)
=>x(3x-1)(3x+1)=0
=>\(\left[{}\begin{matrix}x=0\\3x-1=0\\3x+1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=\dfrac{1}{3}\\x=-\dfrac{1}{3}\end{matrix}\right.\)
3: \(\left(3-2x\right)^2-2\left(2x-3\right)=0\)
=>\(\left(2x-3\right)^2-2\left(2x-3\right)=0\)
=>(2x-3)(2x-3-2)=0
=>(2x-3)(2x-5)=0
=>\(\left[{}\begin{matrix}2x-3=0\\2x-5=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{3}{2}\\x=\dfrac{5}{2}\end{matrix}\right.\)
4: \(\left(2x-5\right)\left(x+5\right)-10x+25=0\)
=>\(2x^2+10x-5x-25-10x+25=0\)
=>\(2x^2-5x=0\)
=>\(x\left(2x-5\right)=0\)
=>\(\left[{}\begin{matrix}x=0\\2x-5=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=\dfrac{5}{2}\end{matrix}\right.\)
Bài 1:
1: \(3x^3y^2-6xy\)
\(=3xy\cdot x^2y-3xy\cdot2\)
\(=3xy\left(x^2y-2\right)\)
2: \(\left(x-2y\right)\left(x+3y\right)-2\left(x-2y\right)\)
\(=\left(x-2y\right)\cdot\left(x+3y\right)-2\cdot\left(x-2y\right)\)
\(=\left(x-2y\right)\left(x+3y-2\right)\)
3: \(\left(3x-1\right)\left(x-2y\right)-5x\left(2y-x\right)\)
\(=\left(3x-1\right)\left(x-2y\right)+5x\left(x-2y\right)\)
\(=(x-2y)(3x-1+5x)\)
\(=\left(x-2y\right)\left(8x-1\right)\)
4: \(x^2-y^2-6y-9\)
\(=x^2-\left(y^2+6y+9\right)\)
\(=x^2-\left(y+3\right)^2\)
\(=\left(x-y-3\right)\left(x+y+3\right)\)
5: \(\left(3x-y\right)^2-4y^2\)
\(=\left(3x-y\right)^2-\left(2y\right)^2\)
\(=\left(3x-y-2y\right)\left(3x-y+2y\right)\)
\(=\left(3x-3y\right)\left(3x+y\right)\)
\(=3\left(x-y\right)\left(3x+y\right)\)
6: \(4x^2-9y^2-4x+1\)
\(=\left(4x^2-4x+1\right)-9y^2\)
\(=\left(2x-1\right)^2-\left(3y\right)^2\)
\(=\left(2x-1-3y\right)\left(2x-1+3y\right)\)
8: \(x^2y-xy^2-2x+2y\)
\(=xy\left(x-y\right)-2\left(x-y\right)\)
\(=\left(x-y\right)\left(xy-2\right)\)
9: \(x^2-y^2-2x+2y\)
\(=\left(x^2-y^2\right)-\left(2x-2y\right)\)
\(=\left(x-y\right)\left(x+y\right)-2\left(x-y\right)\)
\(=\left(x-y\right)\left(x+y-2\right)\)
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 :))))
`a)`
`4x^3 * (-6x^3y)`
`= 4*(-6) * (x^3*x^3) * y`
`= -24x^6y`
`b)`
`(-2y)*(-5xy^2)`
`= (-2)*(-5)*x*(y*y^2)`
`= 10xy^3`
`c)`
`(-2a)^3 * (2ab)^2`
`= (-8a^3) * (4a^2b^2)`
`= (-8*4)*(a^3*a^2)*b^2`
`= -32a^5b^2`
a) \(4x^3\cdot\left(-6x^3y\right)\)
\(=\left(4\cdot-6\right)\cdot\left(x^3\cdot x^3\right)\cdot y\)
\(=-24x^6y\)
b) \(\left(-2y\right)\cdot\left(-5xy^2\right)\)
\(=\left(-2\cdot-5\right)\cdot\left(y\cdot y^2\right)\cdot x\)
\(=10xy^3\)
c) \(\left(-2a\right)^3\cdot\left(2ab\right)^2\)
\(=-8a^3\cdot4a^2b^2\)
\(=\left(-8\cdot4\right)\cdot\left(a^3\cdot a^2\right)\cdot b^2\)
\(=-32a^5b^2\)