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Viết lại :
a) \(M=\left(x+y\right)^3+2\left(x+y\right)^2\)
b) \(N=\left(x-y\right)^3-\left(x-y\right)^2\)
a) M=(x+y)3+2x2+4xy+2y2
M=73+(2x+2y)2=4(x+y)2=73+4.72=343+196=539
b)N=(x-y)3-x2+2xy-y2
N=-53-(x2-2xy+y2)=-125-(x-y)2=-125-(-5)2=-150
B=....
<=>B=x^3+y^3+3xy(x+y)-2(x^2+y^2+2xy)+3(x+y)+10
<=>B=(x+y)^3-2(x+y)^2+3(x+y)+10
tại x+y=5 thay vao B ta đc:
B=5^3-2.5^2+3.5+10
B=100
\(M=x^3+y^3-2\left(x^2+y^2\right)+3xy\left(x+y\right)-4xy+3x+10+3y\)
\(=x^3+y^3-2x^2-2y^2+3x^2y+3xy^2-4xy+3x+10+3y\)
\(=\left(x^3+3x^2y+3xy^2+y^3\right)-2\left(x^2+2xy+y^2\right)+3\left(x+y\right)+10\)
\(=\left(x+y\right)^3-2\left(x+y\right)^2+3\left(x+y\right)+10\)
Ta có: x + y = 5
\(\Rightarrow\left(x+y\right)^3-2\left(x+y\right)^2+3\left(x+y\right)+10=5^3-2.5^2+3.5+10=125-50+15+10=100\)
Vậy M = 100.
A=3(x2+2xy+y2)-2(x+y)-100=3(x+y)2-2.5-100=3.52-110=-35
B=x3+3x2y+3xy2+y3-2(x2+2xy+y2)+3(x+y)+10=(x+y)3-2(x+y)2+3.5+10=53-2.52+25=100
trả lời:
A=3(x2+2xy+y2)-2(x+y)-100
=3(x+y)2-2.5-100
=3.52-110
=-35
B=x3+3x2y+3xy2+y3-2(x2+2xy+y2)+3(x+y)+10
=(x+y)3-2(x+y)2+3.5+10
=53-2.52+25
=100
học tốt
bài 1
a) \(7x\left(5x-1\right)+5x-1=\left(5x-1\right)\left(7x+1\right)\)
b) \(4xy-4x^2-y^2+25=25-\left(4x^2-4xy+y^2\right)\)
\(=5^2-\left(2x-y\right)=\left(5-2x+y\right)\left(5+2x-y\right)\)
c) \(2x^2-2y+xy-4x=\left(2x^2+xy\right)-\left(2y+4x\right)\)
\(=x^2\left(2x+y\right)-2\left(2x+y\right)=\left(2x+y\right)\left(x^2-2\right)\)
d) \(3x^2-7x+2=3x^2-6x-x+2\)
\(=3x\left(x-2\right)-\left(x-2\right)\)
\(=\left(x-2\right)\left(3x-1\right)\)
bài 2
a) * Rút gọn:
\(Q=3\left(2x-1\right)^2+2\left(2x+3\right)\left(x-1\right)-\left(x-3\right)\left(x+3\right)\)
\(Q=\left[3\left(4x^2-4x+1\right)\right]+\left[2\left(2x^2-2x+3x-3\right)\right]-\left(x^2-9\right)\)
\(Q=\left(12x^2-12x+3\right)+\left(4x^2-4x+6x-6\right)-\left(x^2-9\right)\)
\(Q=12x^2-12x+3+4x^2-4x+6x-6-x^2+9\)
\(Q=15x^2-10x+6=5x\left(3x-2\right)+6\)
Thế x = 2 vào biểu thức Q ta được:
\(Q=5\cdot2\left(3\cdot2-2\right)+6=46\)
b) \(Q=5x\left(3x-2\right)+6=6\)
\(\Leftrightarrow5x\left(3x-2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}5x=0\\3x-2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=\dfrac{2}{3}\end{matrix}\right.\)
A = ( x + y )3 + 2x2 + 4xy + 2y2
A = 53 + 2 ( x2 + 2xy + y2 )
A = 125 + 2 ( x + y )2
A = 125 + 2 . 52
A = 125 + 2 . 25
A = 125 + 50 = 175
\(A=\left(x+y\right)^3+2x^2+4xy+2y^2\)
\(=\left(x+y\right)^3+2\left(x^2+2xy+y^2\right)\)
\(=\left(x+y\right)^3+2\left(x+y\right)^2\)
\(=7^3+2\cdot7^2=441\)