K
Khách
Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
Các câu hỏi dưới đây có thể giống với câu hỏi trên
17 tháng 10 2019
a) \(x^2+y^2=\left(x+y\right)^2-2xy=15^2-2.56\)\(=113\)
b) \(a^3+b^3=\left(a+b\right)^3-3ab\left(a+b\right)=10^3-3.21.10=370\)
15 tháng 10 2017
\(a,16x^2-4y^2\)
\(=\left(4x\right)^2-\left(2y\right)^2\)
\(=\left(4x-2y\right)\left(4x+2y\right)\)
\(=\left[2\left(2x-y\right)\right]\left[2\left(2x+y\right)\right]\)
\(=4\left(2x-y\right)\left(2x+y\right)\)
\(b,mx-my-nx+ny+y^2-2xy+x^2\)
\(=\left(mx-my\right)-\left(nx-ny\right)+\left(y^2-2xy+x^2\right)\)
\(=m\left(x-y\right)-n\left(x-y\right)+\left(x-y\right)^2\)
\(=\left(x-y\right)\left(m-n-x+y\right)\)
\(c,\left(x+y+z\right)^3-x^3-y^3-z^3\)
\(=\left[\left(x+y+z\right)^3-x^3\right]-\left[y^3+z^3\right]\)
\(=\left(x+y+z-x\right)\left[\left(x+y+z\right)^2+\left(x+y+z\right)x+x^2\right]-\left(y+z\right)\left(y^2-yz+z^2\right)\)
\(=\left(y+z\right)\left[\left(x+y+z\right)^2+x^2+xy+z^2-y^2+yz-z^2\right]\)
\(=\left(y+z\right)\left(x^2+y^2+z^2+2xy+2xz+2yz+x^2+xy+z^2-y^2+yz-z^2\right)\)
\(=\left(y+z\right)\left(2x^2+z^2+3xy+3yz+2xz\right)\)
NN
1 tháng 12 2017
a) \(\dfrac{2x}{x^2+2xy}+\dfrac{y}{xy-2y^2}+\dfrac{4}{x^2-4y^2}\)
\(=\dfrac{2x}{x\left(x+2y\right)}+\dfrac{y}{y\left(x-2y\right)}+\dfrac{4}{\left(x-2y\right)\left(x+2y\right)}\) MTC: \(xy\left(x-2y\right)\left(x+2y\right)\)
\(=\dfrac{2x.y\left(x-2y\right)}{xy\left(x+2y\right)\left(x-2y\right)}+\dfrac{y.x\left(x+2y\right)}{xy\left(x-2y\right)\left(x+2y\right)}+\dfrac{4.xy}{xy\left(x-2y\right)\left(x+2y\right)}\)
\(=\dfrac{2xy\left(x-2y\right)+xy\left(x+2y\right)+4xy}{xy\left(x+2y\right)\left(x-2y\right)}\)
\(=\dfrac{2x^2y-4xy^2+x^2y+2xy^2+4xy}{xy\left(x+2y\right)\left(x-2y\right)}\)
\(=\dfrac{3x^2y-2xy^2+4xy}{xy\left(x+2y\right)\left(x-2y\right)}\)
b) \(\dfrac{1}{x-y}+\dfrac{3xy}{y^3-x^3}+\dfrac{x-y}{x^2+xy+y^2}\)
\(=\dfrac{1}{x-y}-\dfrac{3xy}{x^3-y^3}+\dfrac{x-y}{x^2+xy+y^2}\)
\(=\dfrac{1}{x-y}-\dfrac{3xy}{\left(x-y\right)\left(x^2+xy+y^2\right)}+\dfrac{x-y}{x^2+xy+y^2}\) MTC: \(\left(x-y\right)\left(x^2+xy+y^2\right)\)
\(=\dfrac{x^2+xy+y^2}{\left(x-y\right)\left(x^2+xy+y^2\right)}-\dfrac{3xy}{\left(x-y\right)\left(x^2+xy+y^2\right)}+\dfrac{\left(x-y\right)\left(x-y\right)}{\left(x-y\right)\left(x^2+xy+y^2\right)}\)
\(=\dfrac{\left(x^2+xy+y^2\right)-3xy+\left(x-y\right)^2}{\left(x-y\right)\left(x^2+xy+y^2\right)}\)
\(=\dfrac{x^2+xy+y^2-3xy+x^2-2xy+y^2}{\left(x-y\right)\left(x^2+xy+y^2\right)}\)
\(=\dfrac{2x^2-4xy+2y^2}{\left(x-y\right)\left(x^2+xy+y^2\right)}\)
\(=\dfrac{2\left(x^2-2xy+y^2\right)}{\left(x-y\right)\left(x^2+xy+y^2\right)}\)
\(=\dfrac{2\left(x-y\right)^2}{\left(x-y\right)\left(x^2+xy+y^2\right)}\)
\(=\dfrac{2\left(x-y\right)}{x^2+xy+y^2}\)
21 tháng 5 2022
a: \(=x^3-3x^2+3x-1-x^3-64+3x^2-3x\)
=-65
b \(=8x^3+27y^3-8x^3+27y^3-54y^3+27\)
=27
c: \(=y\left(x^4-y^4\right)-y\left(x^4-y^4\right)=0\)
d: \(=x^3-3x^2+3x-1-x^3+1-3x\left(1-x\right)\)
\(=-3x^2+3x-3x+3x^2=0\)
MN
4
KT
19 tháng 7 2018
6) \(9x^2+6xy+y^2=\left(3x+y\right)^2\)
7) \(x^2-3x-y^2-3y=\left(x-y-3\right)\left(x+y\right)\)
8) \(x^2-2xy+y^2-16=\left(x-y\right)^2-16=\left(x-y-4\right)\left(x-y+4\right)\)
9) \(4x^2-y^2+4x+1=\left(2x+1\right)^2-y^2=\left(2x-y+1\right)\left(2x+y+1\right)\)
10) \(x^3-x+y^3-y=\left(x+y\right)\left(x^2-xy+y^2+1\right)\)
19 tháng 7 2018
6) = (3x)2 + 2.(3x)y +y2 = (3x + y)2
7) = (x-y)(x+y)- 3(x+y) = (x+y)(x-y-3)
8) = (x-y)2 - 42 = (x-y-4)(x-y+4)
9) = ( 4x2 + 4x +1 ) - y2 = (2x+1)2 - y^2 = (2x+1-y)(2x+1+y)
10) =(x3+y3) - (x+y) = (x+y)(x2+xy+y2) - (x+y) = (x+y)(x2+xy+y2-1)
k mk đi nha
29 tháng 10 2017
1,Thực hiện phép tính :
a, (x + 2)9 : (x + 2)6
=(x+2)9-6
=(x+2)3
b, (x - y) 4 : (x - 2)3
=(x-y)4-3
=x-y
c, ( x2+ 2x + 4)5 : (x2 + 2x + 4)
=(x2+2x+4)5-1
=(x2+2x+4)4
d, 2(x2 + 1)3 : 1/3(x2 + 1)
=(2÷1/3).[(x2+1)3÷(x2+1)]
=6(x2+1)2
e, 5 (x - y)5 : 5/6 (x - y)2
=(5÷5/6).[(x-y)5÷(x-y)2]
=6(x-y))3
\(56x^3+16y^3\)
\(\Leftrightarrow8\left(7x^3+2y^3\right)\)