Rút gọn biểu thức
(x+y)^2+(x-y)
2(x-y)(x+y)+(x+y)^2+(x-y)^2
(2x-y)^3+(2x+y)^3
K
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Những câu hỏi liên quan
Y
29 tháng 6 2023
\(1,\left(x+y\right)^2-\left(x-y\right)^2=\left[\left(x+y\right)-\left(x-y\right)\right]\left[\left(x+y\right)+\left(x-y\right)\right]=\left(x+y-x+y\right)\left(x+y+x-y\right)=2y.2x=4xy\)
\(2,\left(x+y\right)^3-\left(x-y\right)^3-2y^3\)
\(=x^3+3x^2y+3xy^2+y^3-x^3+3x^2y-3xy^2+y^3-2y^3\)
\(=6x^2y\)
\(3,\left(x+y\right)^2-2\left(x+y\right)\left(x-y\right)+\left(x-y\right)^2\\ =\left[\left(x+y\right)-\left(x-y\right)\right]^2\\ =\left(x+y-x+y\right)^2\\ =4y^2\)
\(4,\left(2x+3\right)^2-2\left(2x+3\right)\left(2x+5\right)+\left(2x+5\right)^2\\ =\left[\left(2x+3\right)-\left(2x+5\right)\right]^2\\ =\left(2x+3-2x-5\right)^2\\ =\left(-2\right)^2\\ =4\)
\(5,9^8.2^8-\left(18^4+1\right)\left(18^4-1\right)\\ =18^8-\left[\left(18^4\right)^2-1\right]\\ =18^8-18^8+1\\ =1\)
29 tháng 6 2023
1: =x^2+2xy+y^2-x^2+2xy-y^2=4xy
2: =x^3+3x^2y+3xy^2+y^3-x^3+3x^2y-3xy^2+y^3-2y^3
=6x^2y
3: =(x+y-x+y)^2=(2y)^2=4y^2
4: =(2x+3-2x-5)^2=(-2)^2=4
5: =18^8-18^8+1=1
5 tháng 12 2023
a: \(F=-\left(2x-y\right)^3-x\left(2x-y\right)^2-y^3\)
\(=-\left(2x-y\right)^2\cdot\left[2x-y+x\right]-y^3\)
\(=-\left(2x-y\right)^2\cdot\left(3x-y\right)-y^3\)
\(=\left(-4x^2+4xy-y^2\right)\left(3x-y\right)-y^3\)
\(=-12x^3+4x^2y+12x^2y-4xy^2-3xy^2+y^3-y^3\)
\(=-12x^3+16x^2y-7xy^2\)
\(\left(x-2\right)^2+y^2=0\)
mà \(\left(x-2\right)^2+y^2>=0\forall x,y\)
nên dấu '=' xảy ra khi \(\left\{{}\begin{matrix}x-2=0\\y=0\end{matrix}\right.\)
=>x=2 và y=0
Thay x=2 và y=0 vào F, ta được:
\(F=-12\cdot2^3+16\cdot2^2\cdot0-7\cdot2\cdot0^2\)
\(=-12\cdot2^3\)
\(=-12\cdot8=-96\)
b: \(G=\left(x+y\right)\left(x^2-xy+y^2\right)+3\left(2x-y\right)\left(4x^2+2xy+y^2\right)\)
\(=x^3+y^3+3\left(2x-y\right)\left[\left(2x\right)^2+2x\cdot y+y^2\right]\)
\(=x^3+y^3+3\left(8x^3-y^3\right)\)
\(=x^3+y^3+24x^3-3y^3\)
\(=25x^3-2y^3\)
Ta có: \(\left\{{}\begin{matrix}x+y=2\\y=-3\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}y=-3\\x=2-y=2-\left(-3\right)=2+3=5\end{matrix}\right.\)
Thay x=5 và y=-3 vào G, ta được:
\(G=25\cdot5^3-2\cdot\left(-3\right)^3\)
\(=25\cdot125-2\cdot\left(-27\right)\)
\(=3125+54=3179\)
c: \(H=\left(x+3y\right)\left(x^2-3xy+9y^2\right)+\left(3x-y\right)\left(9x^2+3xy+y^2\right)\)
\(=\left(x+3y\right)\left[x^2-x\cdot3y+\left(3y\right)^2\right]+\left(3x-y\right)\left[\left(3x\right)^2+3x\cdot y+y^2\right]\)
\(=x^3+27y^3+27x^3-y^3\)
\(=28x^3-26y^3\)
Ta có: \(\left\{{}\begin{matrix}3x-y=5\\x=2\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x=2\\y=3x-5=3\cdot2-5=1\end{matrix}\right.\)
Thay x=2 và y=1 vào H, ta được:
\(H=28\cdot2^3-26\cdot1^3\)
\(=28\cdot8-26\)
=198
3 tháng 9 2021
\(a,\left(2x-1\right)^2-\left(x-3\right)\left(x+3\right)-1969\\ =4x^2-4x+1-x^2+9-1969\\ =3x^2-4x-1959\)
\(b,\left(2x-3y\right)\left(2x+3y\right)-\left(2x-y\right)^2\\ =4x^2-9y^2-4x^2+4xy-y^2\\ =8y^2+4xy=4y\left(2y+x\right)\)
\(c,\left(x+3y\right)^2+\left(x+y\right)\left(x-y\right)+280\\ =x^2+6xy+9y^2+x^2-y^2+280\\ =2x^2+8y^2+6xy+280\)
3 tháng 9 2021
a: \(\left(2x-1\right)^2-\left(x-3\right)\cdot\left(x+3\right)-1969\)
\(=4x^2-4x+1-x^2+9-1969\)
\(=3x^2-4x-1959\)
b: \(\left(2x-3y\right)\left(2x+3y\right)-\left(2x-y\right)^2\)
\(=4x^2-9y^2-4x^2+4xy-y^2\)
\(=-10y^2+4xy\)
NV
4
GP
14 tháng 7 2021
a) (x+3)(x^2-3x+9)-(54+x^3)
= x^3- 3x^2+9x+3x^2-9x+27-54-x63
= -27
b) (2x + y)(4x^2 – 2xy + y^2) – (2x – y)(4x^2+ 2xy + y^2)
= (2x + y)[(2x)^2 – 2x.y + y^2] – (2x – y)[(2x)^2 + 2x.y + y^2]
= [(2x)3^3+ y^3] – [(2x)^3 – y^3]
= (2x)^3 + y^3 – (2x)^3 + y^3
= 2y^3
GS
14 tháng 7 2021
a)(x+3)(X^2-3x+9)-(54+x^3)
= \(x^3\)+ \(3^3 \) - 54 -\(x^3\)
= 27- 54
= -27
b)(2x+y)(4x^2-2xy+y^2)-(2x-y)(4x^2+2xy+y^2)
= \((2x)^3\) + \(y^3\) - [\((2x)^3\) - \(y^3\) ]
= \(8x^3\) + \(y^3\) - \(8x^3\) + \(y^3\)
= \(2y^3\)
17 tháng 4 2021
Ta có: \(\dfrac{x^2+xy}{x^2+xy+y^2}-\left(\dfrac{x\left(2x^2+xy-y^2\right)}{x^3-y^3}-2+\dfrac{y}{y-x}\right):\dfrac{x-y}{x}-\dfrac{x}{x-y}\)
\(=\dfrac{x^2+xy}{x^2+xy+y^2}-\left(\dfrac{x\left(2x^2+xy-y^2\right)}{\left(x-y\right)\left(x^2+xy+y^2\right)}-\dfrac{2\left(x^3-y^3\right)-y\left(x^2+xy+y^2\right)}{\left(x-y\right)\left(x^2+xy+y^2\right)}\right):\dfrac{x-y}{x}-\dfrac{x}{x-y}\)
\(=\dfrac{x^2+xy}{x^2+xy+y^2}-\dfrac{2x^3+x^2y-xy^2-2x^3+2y^3-x^2y-xy^2-y^3}{\left(x-y\right)\left(x^2+xy+y^2\right)}:\dfrac{x-y}{x}-\dfrac{x}{x-y}\)
\(=\dfrac{x\left(x+y\right)}{x^2+xy+y^2}-\dfrac{y^3-2xy^2}{\left(x-y\right)\left(x^2+xy+y^2\right)}:\dfrac{x-y}{x}-\dfrac{x}{x-y}\)
\(=\dfrac{x\left(x+y\right)}{x^2+xy+y^2}+\dfrac{y^2\left(x-y\right)}{\left(x-y\right)\left(x^2+xy+y^2\right)}\cdot\dfrac{x}{x-y}-\dfrac{x}{x-y}\)
\(=\dfrac{x\left(x+y\right)}{x^2+xy+y^2}+\dfrac{xy^2}{\left(x-y\right)\left(x^2+xy+y^2\right)}-\dfrac{x}{x-y}\)
\(=\dfrac{x\left(x^2-y^2\right)}{\left(x-y\right)\left(x^2+xy+y^2\right)}+\dfrac{xy^2}{\left(x-y\right)\left(x^2+xy+y^2\right)}-\dfrac{x\left(x^2+xy+y^2\right)}{\left(x-y\right)\left(x^2+xy+y^2\right)}\)
\(=\dfrac{x^3-xy^2+xy^2-x^3-x^2y-xy^2}{\left(x-y\right)\left(x^2+xy+y^2\right)}\)
\(=\dfrac{-x^2y-xy^2}{\left(x-y\right)\left(x^2+xy+y^2\right)}\)
VH
1
10 tháng 8 2015
a) 3.(x+y).(x-y)+(x+y)^2+(x-y)^2
=3.(x2-y2)+(x2+2xy+y2)+(x2-2xy+y2)
=3x2-3y2+x2+2xy+y2+x2-2xy+y2
=5x2-y2
b) (2x+y)^2 - (y+3x)^2
=[(2x+y)+(y+3x)][(2x+y)-(y+3x)]
=(2x+y+y+3x)(2x+y-y-3x)
=(5x+2y)(-x)
=-5x2-2xy
LN
1
TN
13 tháng 6 2019
a/\(\left(2x-1\right)^2-2\left(2x-3\right)^2+4\)
\(=4x^2-4x+1-2\left(4x^2-12x+9\right)+4\)
\(=4x^2-4x+1-8x^2+24x-18+4\)
\(=-4x^2+20x-13\)
b/ \(2\left(x-y\right)\left(x+y\right)+\left(x+y\right)^2+\left(x-y\right)^2\)
\(=2\left(x^2-y^2\right)+x^2+2xy+y^2+x^2-2xy+y^2\)
\(=2x^2-2y^2+2x^2+2y^2\)
\(=4x^2\)
chúc bạn học tốt
PH
25 tháng 10 2015
a) (x+y+x_y).(x+y_x+y)
b ) (( x + y )+(x _ y))2
d ) 8x3 + y3 _ 8x3 + y3 =2y3
26 tháng 6 2019
\(a,\left(x-2\right)^3-x\left(x-1\right)\left(x+1\right)+6x\left(x-3\right)\)
\(=x^3-6x^2+12x-27-x^3+x+6x^2-18x\)
\(=-5x-27\)
\(b,\left(2x+y\right)\left(4x^2-2xy+y^2\right)-\left(2x-y\right)\left(4x^2+2xy+y^2\right)\)
\(=8x^3+y^3-\left(8x^3-y^3\right)\)
\(=8x^3+y^3-8x^3+y^3=2y^3\)
\(\left(x+y+z\right)^2-2\left(x+y+z\right)\left(x+y\right)+\left(x+y\right)^2\)
\(=\left(x+y+z-x-y\right)^2\)
\(=z^2\)
26 tháng 6 2019
a)
=\(x^3-6x^2+12x+8-27-x^3+x+6x^2-18x\)
=-5x-19
b)
=\(8x^3+y^3-8x^3+y^3\)
=\(2y^3\)
c)
=(x+y+z-x-y)\(^2\) +x+y
=\(z^2+x+y\)
hc tốt
NV
Nguyễn Việt Lâm
Giáo viên
23 tháng 12 2022
\(A=\dfrac{2x}{x\left(x+y\right)}+\dfrac{6x}{\left(x-y\right)\left(x+y\right)}-\dfrac{3}{x-y}\)
\(=\dfrac{2\left(x-y\right)}{\left(x-y\right)\left(x+y\right)}+\dfrac{6x}{\left(x-y\right)\left(x+y\right)}-\dfrac{3\left(x+y\right)}{\left(x+y\right)\left(x-y\right)}\)
\(=\dfrac{2x-2y+6x-3x-3y}{\left(x-y\right)\left(x+y\right)}=\dfrac{5\left(x-y\right)}{\left(x-y\right)\left(x+y\right)}\)
\(=\dfrac{5}{x+y}\)
\(=x^2+2xy+y^2+x-y\)
\(=\left(x+y+x-y\right)^2=4x^2\)
\(=\left(2x-y+2x+y\right)^3+3\left(2x-y\right)\left(2x+y\right)\left(2x-y+2x+y\right)=64x^3+3\left(4x^2-y^2\right).4x\)
\(=64x^3+12x\left(4x^2-y^2\right)=64x^3+48x^3-12xy^2=11x^3-12xy\)