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a)
\(\begin{array}{l}\left( {2x - 5y} \right)\left( {2x + 5y} \right) + {\left( {2x + 5y} \right)^2}\\ = \left( {2x + 5y} \right)\left( {2x - 5y + 2x + 5y} \right)\\ = \left( {2x + 5y} \right).4x\\ = 2x.4x + 5y.4x\\ = 8{x^2} + 20xy\end{array}\)
b)
\(\begin{array}{l}\left( {x + 2y} \right)\left( {{x^2} - 2xy + 4{y^2}} \right) + \left( {2x - y} \right)\left( {4{x^2} + 2xy + {y^2}} \right)\\ = {x^3} + {\left( {2y} \right)^3} + {\left( {2x} \right)^3} - {y^3}\\ = {x^3} + 8{y^3} + 8{x^3} - {y^3}\\ = \left( {{x^3} + 8{x^3}} \right) + \left( {8{y^3} - {y^3}} \right)\\ = 9{x^3} + 7{y^3}\end{array}\)
a) (x2 – 2x + 3) (1212x – 5)
= 1212x3 - 5x2 - x2 +10x + 3232x – 15
= 1212x3 – 6x2 + 232232x -15
b) (x2 – 2xy + y2)(x – y)
= x3 - x2 y - 2x2 y + 2xy2 +xy2- y3
= x3 - 3x2 y + 3xy2 - y3
a) (x2 – 2x + 3) ( 1/2x – 5) = \(\dfrac{1}{2}\)x3 – 5x2 – x2 + 10x +\(\dfrac{3}{2}\)x - 15
= \(\dfrac{1}{2}\)x3 – 6x2 + \(\dfrac{23}{2}\) x – 15.
b) (x2 – 2xy + y2)( x – y) = x3 – x2y – 2x2y + xy2 – y3 = x3 – 3x2y + 3xy2 – y3
`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`
a)
\(\begin{array}{l}\left( {2x + y} \right)\left( {4{x^2} - 2xy + {y^2}} \right)\\ = 2x.4{x^2} - 2x.2xy + 2x.{y^2} + y.4{x^2} - y.2xy + y.{y^2}\\ = 8{x^3} - 4{x^2}y + 2x{y^2} + 4{x^2}y - 2x{y^2} + {y^3}\\ = 8{x^3} + \left( { - 4{x^2}y + 4{x^2}y} \right) + \left( {2x{y^2} - 2x{y^2}} \right) + {y^3}\\ = 8{x^3} + {y^3}\end{array}\)
b)
\(\begin{array}{l}\left( {{x^2}{y^2} - 3} \right)\left( {3 + {x^2}{y^2}} \right)\\ = {x^2}{y^2}.3 + {x^2}{y^2}.{x^2}{y^2} - 3.3 - 3.{x^2}{y^2}\\ = 3{x^2}{y^2} + {x^4}{y^4} - 9 - 3{x^2}{y^2}\\ = {x^4}{y^4} + \left( {3{x^2}{y^2} - 3{x^2}{y^2}} \right) - 9\\ = {x^4}{y^4} - 9\end{array}\)
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) \(\left(x+3y\right)\left(2x^2y-6xy^2\right)\)
\(=x\left(2x^2y-6xy^2\right)+3y\left(2x^2y-6xy^2\right)\)
\(=2x^3y-6x^2y^2+6x^2y^2-18xy^3\)
\(=2x^3y-18xy^3\)
b) \(\left(6x^5y^2-9x^4y^3+15x^3y^4\right):3x^3y^2\)
\(=6x^5y^2:3x^3y^2-9x^4y^3:3x^3y^2+15x^3y^4:3x^3y^2\)
\(=2x^2-3xy+5y^2\)
c) \(\left(2x+3\right)^2+\left(2x+5\right)^2-2\left(2x+3\right)\left(2x+5\right)\)
\(=\left(2x+3-2x-5\right)^2\)
\(=\left(-2\right)^2=4\)
d) \(\left(y+3\right)^3-\left(3-y\right)^2-54y\)
\(=y^3+9y^2+27y+27-\left(x^2-6x+9\right)-54y\)
\(=y^3+9y^2-27y+27-x^2+6y-9\)
\(=y^3+9y^2-x^2-21y+18\)
a) (x2 + 2xy + y2) : (x + y) = (x + y)2 : (x + y) = x + y.
b) (125x3 + 1) : (5x + 1) = [(5x)3 + 1] : (5x + 1)
= (5x)2 – 5x + 1 = 25x2 – 5x + 1.
c) (x2 – 2xy + y2) : (y – x) = (x – y)2 : [-(x – y)] = - (x – y) = y – x
Hoặc (x2 – 2xy + y2) : (y – x) = (y2 – 2xy + x2) : (y – x)
= (y – x)2 : (y – x) = y - x.
Bài giải:
a) (x2 + 2xy + y2) : (x + y) = (x + y)2 : (x + y) = x + y.
b) (125x3 + 1) : (5x + 1) = [(5x)3 + 1] : (5x + 1)
= (5x)2 – 5x + 1 = 25x2 – 5x + 1.
c) (x2 – 2xy + y2) : (y – x) = (x – y)2 : [-(x – y)] = - (x – y) = y – x
Hoặc (x2 – 2xy + y2) : (y – x) = (y2 – 2xy + x2) : (y – x)
= (y – x)2 : (y – x) = y - 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) \(\left(2x+y\right)\left(4x^2-2xy+y^2\right)\)
\(=8x^3-4x^2y+2xy^2+4x^2y-2xy^2+y^3\)
\(=8x^3+y^3\)