Rút gọn các biểu thức sau:
10) (2x+1)^2+(-3x-1)^2
11) -(x-y)^2-(2x+y)^2
12) (2x+7)^2+(-2x-3)^2
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25 tháng 2 2021
`a,(25xy^3(2x-y)^2)/(75xy^2(y-2x))(x,y ne 0)(y ne 2x)`
`=(25xy^3(y-2x)^2)/(75xy^2(y-2x))`
`=(y(y-2x))/3`
`b,(x^2-y^2)/(x^2-y^2+xz-yz)`
`=((x-y)(x+y))/((x-y)(x+y)+z(x-y))`
`=(x+y)/(x+y+z)`
`c,((2x+3)-x^2)/(x^2-1)(x ne +-1)`
`=(-(x^2-3x+x-3))/((x-1)(x+1))`
`=(-x(x-3)+x-3)/((x-1)(x+1))`
`=((x-3)(1-x))/((x-1)(x+1))`
`=(3-x)/(1+x)`
`d,(3x^3-7x^2+5x-1)/(2x^3-x^2-4x+3)`
`=(3x^3-3x^2-4x^2+4x+x-1)/(2x^3-2x^2+x^2-x-3x+3)`
`=(3x^2(x-1)-4x(x-1)+x-1)/(2x^2(x-1)+x(x-1)-3(x-1))`
`=(3x^2-4x+1)/(2x^2+x-3)`
`=(3x^2-3x-x+1)/(2x^2-2x+3x-3)`
`=(3x(x-1)-(x-1))/(2x(x-1)+3(x-1))`
`=(3x-1)/(2x+3)`
25 tháng 2 2021
a) Ta có: \(\dfrac{25xy^3\cdot\left(2x-y\right)^2}{75xy^2\cdot\left(y-2x\right)}\)
\(=\dfrac{25xy^2\cdot y\cdot\left(y-2x\right)^2}{25xy\cdot y\cdot\left(y-2x\right)\cdot3}\)
\(=\dfrac{y\left(y-2x\right)}{3}\)
YN
22 tháng 2 2022
`Answer:`
`a)`
`A=5(x+1)^2-3(x-3)^2-4(x^2-4)`
`=>A=5(x^2+2x+1)-3(x^2-6x+9)-4x^2+16`
`=>A=5x^2+10x+5-3x^2+18x-27-4x^2+16`
`=>A=(5x^2-3x^2-4x^2)+(10x+18x)+(5-27+16)`
`=>A=-2x^2+28x-6`
`b)`
`B=5(x+1)^2-3(x-3)^2-4(x+2)(x-2)`
`=2x(3x+5)-3(3x+5)-2x(x^2-4x+4)-[(2x)^2-3^2]`
`=6x^2+10x-9x-15-2x^3+8x^2-8x-4x^2+9`
`=(6x^2-4x^2+8x^2)-2x^3+(10x-9x-8x)+(-15+9)`
Thay `x=-7` vào ta được:
`B=10(-7)^2-2(-7)^3-7(-7)-6`
`=>B=10.49-2(-343)+49-6`
`=>B=490+686+49-6`
`=>B=1219`
6 tháng 7 2016
a) \(3x^2-2x\left(5+1,5x\right)+10x\)
\(=3x^2-10x-3x^2+10x=0\)
b) \(7x\left(4y-x\right)+4y\left(y-7x\right)-2\left(2y^2-3,5x\right)\)
\(=28xy-7x^2+4y^2-28xy-4y^2+7x\)
\(=-7x^2+7x\)
25 tháng 8 2016
a) 5x2 ( 3x2 -7x+2)-15x(x-3)
=15x4-35x3+10x2-15x2+45x
=15x4-35x3-5x2+45x
c) (x+3)(x-3)(x-2)(x+1)
=(x2-9)(x2+x-2x-2)
=(x2-9)(x2-x-2)
=x4-x3-2x2-9x2+9x+18
=x4-x3-11x2+9x+18
d)(2x+1)2+(4x-1)2+2(2x+1)(4x+1)
=2x2+4x+1-16x2-8x+1
=2x2+4x+1-16x2-8x+1+16x2-4x+8x-2
=2x2+7
e) (2x2-3x)(5x2-2x+1)-10x2(x+3)
=10x4 -4x3+2x2-15x3+6x2-3 -10x2-30x
=10x4-19x3-2x2-30x-3
1 tháng 7 2021
a) Ta có: \(\left(3x-2\right)^2+2\left(3x-2\right)\left(3x+2\right)+\left(3x+2\right)^2\)
\(=\left(3x-2+3x+2\right)^2\)
\(=36x^2\)(1)
Thay \(x=-\dfrac{1}{3}\) vào biểu thức (1), ta được:
\(36\cdot\left(-\dfrac{1}{3}\right)^2=36\cdot\dfrac{1}{9}=4\)
b) Sửa đề: \(\left(x+y-7\right)^2-2\cdot\left(x+y-7\right)\left(y-6\right)+\left(y-6\right)^2\)
Ta có: \(\left(x+y-7\right)^2-2\cdot\left(x+y-7\right)\left(y-6\right)+\left(y-6\right)^2\)
\(=\left(x+y-7-y+6\right)^2\)
\(=\left(x-1\right)^2=100^2=10000\)
10: \(\left(2x+1\right)^2+\left(-3x-1\right)^2\)
\(=4x^2+4x+1+9x^2+6x+1\)
\(=13x^2+10x+2\)
11: \(-\left(x-y\right)^2-\left(2x+y\right)^2\)
\(=-\left(x^2-2xy+y^2\right)-\left(4x^2+4xy+y^2\right)\)
\(=-x^2+2xy-y^2-4x^2-4xy-y^2=-5x^2-2xy-2y^2\)
12: \(\left(2x+7\right)^2+\left(-2x-3\right)^2\)
\(=\left(2x+7\right)^2+\left(2x+3\right)^2\)
\(=4x^2+28x+49+4x^2+12x+9=8x^2+40x+58\)
10) \(\left(2x+1\right)^2+\left(-3x-1\right)^2\)
\(=\left(4x^2+4x+1\right)+\left(9x^2+6x+1\right)\)
\(=4x^2+4x+1+9x^2+6x+1\)
\(=\left(4x^2+9x^2\right)+\left(4x+6x\right)+\left(1+1\right)\)
\(=13x^2+10x+2\)
11) \(-\left(x-y\right)^2-\left(2x+y\right)^2\)
\(=-\left\lbrack\left(x-y\right)^2+\left(2x+y\right)^2\right\rbrack\)
\(=-\left\lbrack\left(x^2-2xy+y^2\right)+\left(4x^2+4xy+y^2\right)\right\rbrack\)
\(=-\left\lbrack x^2-2xy+y^2+4x^2+4xy+y^2\right\rbrack\)
\(=-\left\lbrack\left(x^2+4x^2\right)+\left(-2xy+4xy\right)+\left(y^2+y^2\right)\right\rbrack\)
\(=-\left\lbrack5x^2+2xy+2y^2\right\rbrack\)
\(=-5x^2-2xy-2y^2\)
12) \(\left(2x+7\right)^2+\left(-2x-3\right)^2\)
\(=\left(4x^2+28x+49\right)+\left(4x^2+12x+9\right)\)
\(=4x^2+28x+49+4x^2+12x+9\)
\(=\left(4x^2+4x^2\right)+\left(28x+12x\right)+\left(49+9\right)\)
\(=8x^2+40x+58\)