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`a, 20x^3y^5 : 5x^2y^2`
`= (20:5)x^(3-2) . y^(5-2)`
`= 4xy^3`
`b, 18x^3y^5 : (3(-x^3)y^2)`
`= -(18:3)y^(5-3)`
`= -6y^2`
`a, (5ab - 2a^2):a`
`= 5b - 2a`
`b, (6x^2y^2-xy^2+3x^2y) : (-3xy)`
`= -2xy + y/3 - x`.
`a, (x-y)(x-5y)`
`= x^2 - xy - 5xy + 5y^2`
`= x^2 - 6xy + 5y^2`
`b, (2x+y)(4x^2 -2xy + y^2)`
`= (2x)^3 + y^3`
`= 8x^3 + y^3`
a) \(\left(x-y\right)\left(x-5y\right)\)
\(=x^2-5xy-xy+5y^2\)
\(=x^2-6xy+5y^2\)
b) \(\left(2x+y\right)\left(4x^2-2xy+y^2\right)\)
\(=8x^3-4x^2y+2xy^2+4x^2y-2xy^2+y^3\)
\(=8x^3+y^3\)
\(a,=5^3:5^2=5\\ b,=\left(\dfrac{3}{4}\right)^{5-3}=\left(\dfrac{3}{4}\right)^2=\dfrac{9}{16}\\ c,=1728-512=1216\\ d,=x^{10}:x^8=x^2\\ e,=\left(-x\right)^{5-3}=\left(-x\right)^2=x^2\\ f,=\left(-y\right)^{5-4}=-y\)
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`
a) \(18x^4y^3:12\left(-x\right)^3y\)
\(=\left(18:-12\right)\left(x^4:x^3\right)\left(y^3:y\right)\)
\(=-\dfrac{3}{2}xy^2\)
b) \(x^2y^2-2xy^3:\dfrac{1}{2}xy^2\)
\(=\dfrac{xy^2\left(x-2y\right)}{\dfrac{1}{2}xy^2}\)
\(=\dfrac{x-2y}{\dfrac{1}{2}}\)
\(=2x-4y\)
`a)`
`3x(2xy - 5x^2y)`
`= 3x*2xy + 3x* (-5x^2y)`
`= 6x^2y - 15x^3y`
`b)`
`2x^2y (xy - 4xy^2 + 7y)`
`= 2x^2y * xy + 2x^2y * (-4xy^2) + 2x^2y * 7y`
`= 2x^3y^2 - 8x^3y^3 + 14x^2y^2`
`c)`
`(-2/3xy^2 + 6yz^2)*(-1/2xy)`
`= (-2/3xy^2)*(-1/2xy) + 6yz^2 * (-1/2xy)`
`= 1/3x^2y^3 - 3xy^2z^2`
`a, 3x(2xy-5x^2y)`
`= 6x^2y - 15x^3y`
`b, 2x^2y(xy-4xy^2+7y)`
`= 2x^3y^2 - 8x^3y^3 + 14x^2y^2`
`c, (-2/3xy^2 + 6yz^2).(-1/2xy)`
`= 1/3x^2y^3 - 3xy^2z^2`
a) =(x-y)5+(x-y)3=(x-y)3[(x-y)2+1]
b) =33(y-2x)3:-9(y-2x)=-3(y-2x)2
c) =(x-y)2 [3(x-y)3-2(x-y)2+3]:5(x-y)2=[3(x-y)3-2(x-y)2+3]/5
`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, (4x^3y^2 - 8x^2y + 10xy) : 2xy`
`= 2x^2y - 4x + 5`.
`b, 7x^4y^2 - 2x^2y^2 - 5x^3y^4 : 3x^2y`
`= 7/3 x^2y - 3/2y - 5/3xy^3`