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Q
14 tháng 6 2017
1) \(-4x^5\left(x^3-4x^2+7x-3\right)\)
\(=-4x^8+16x^7-28x^6+12x^5\)
2) \(3x^4\left(-2x^3+5x^2-\dfrac{2}{3}x+\dfrac{1}{3}\right)\)
\(=-6x^7+15x^6-2x^5+x^4\)
3) \(-5x^2y^4\left(3x^2y^3-2x^3y^2-xy\right)\)
\(=-15x^4y^7+10x^5y^6+5x^3y^5\)
4) \(4x^3y^2\left(-2x^2y+4x^4-3y^2\right)\)
\(=-8x^5y^3+16x^7y^2-12x^3y^4\)
P
1) Viết biểu thức sau dưới dạng hiệu 2 bình phương:
a)4x2+6x+7-y2-6y
b)x2+y2-4x-6y+13
c)4x2-12x-y2+2y+8
2
KT
18 tháng 7 2018
b) \(x^2+y^2-4x-6y+13\)
\(=\left(x^2-4x+4\right)+\left(y^2-6y+9\right)\)
\(=\left(x-2\right)^2+\left(y-3\right)^2\)
c) \(4x^2-12x-y^2+2y+8\)
\(=\left(4x^2-12x+9\right)-\left(y^2-2y+1\right)\)
\(=\left(2x-3\right)^2-\left(y-1\right)^2\)
28 tháng 9 2018
\(x^2+y^2-4x-6y+13\)
\(=\left(x^2-4x+4\right)+\left(y^2-6y+9\right)\)
\(=\left(x-2\right)^2+\left(y-3\right)^2\)
hk
22 tháng 9 2020
a) Ta có: \(\left(x+y\right)^2-8\left(x+y\right)+12\)
\(=\left[\left(x+y\right)^2-8\left(x+y\right)+16\right]-4\)
\(=\left(x+y-4\right)^2-4\)
\(=\left(x+y\right)\left(x+y-8\right)\)
4 tháng 8 2019
a,\(-4x^2+4x-1\)
\(\Leftrightarrow\left(-2x-1\right)^2\)
b,\(\left(2x+1\right)^2-4\left(x-1\right)^2\)
\(\Rightarrow\left[2x+1-2\left(x-1\right)\right].\left[2x+1+2\left(x-1\right)\right]\)
\(\Rightarrow\left(2x+1-2x+2\right)\left(2x+1+2x-2\right)\)
\(\Rightarrow3\left(4x-1\right)\)
c,\(\left(2x-y\right)^2-4x^2+12x-9\)
\(\Leftrightarrow\left(2x+y\right)^2-\left(4x^2-12x+9\right)\)
\(\Leftrightarrow\left(2x+y\right)^2-\left(2x-3\right)^2\)
\(\Leftrightarrow\left(2x+y-2x+3\right)\left(2x+y+2x-3\right)\)
\(\Rightarrow\left(y+3\right)\left(4x+y-3\right)\)
d,\(\left(x+1\right)^2-4\left(x+1\right)y^2+4y^4\)
\(\Leftrightarrow\left(x+1\right)^2-2\left(x+1\right)2y^2+2^2y^4\)
\(\Leftrightarrow\left(x+1\right)^2-2\left(x+1\right)2y^2+4\left(y^2\right)^2\)
\(\Leftrightarrow\left(x+1\right)^2-2\left(x+1\right)-2y^2+\left(2y^2\right)^2\)
\(\Leftrightarrow\left(x+1-2y^2\right)^2\)
22 tháng 8 2018
1. \(x^2-2x+2+4y^2+4y\)
\(=\left(x^2-2x+1\right)+\left(4y^2+4y+1\right)\)
\(=\left(x-1\right)^2+\left(2y+1\right)^2\)
2. \(4x^2-4x+y^2+2y+2\)
\(=\left(4x^2-4x+1\right)+\left(y^2+2y+1\right)\)
\(=\left(2x-1\right)^2+\left(y+1\right)^2\)
3. \(4x^2+4x+4y^2+4y+2\)
\(=\left(4x^2+4x+1\right)+\left(4y^2+4y+1\right)\)
\(=\left(2x+1\right)^2+\left(2y+1\right)^2\)
4. \(4x^2+y^2+12x+4y+13\)
\(=\left(4x^2+12x+9\right)+\left(y^2+4y+4\right)\)
\(=\left(2x+3\right)^2+\left(y+2\right)^2\)
3 tháng 9 2018
\(x^2-2x+2+4y^2+4y\)
\(=\left(x^2-2x+1\right)+\left(4y^2+4y+1\right)\)
\(=\left(x-1\right)^2+\left(2y+1\right)^2\)
\(4x^2-4x+y^2+2y+2\)
\(=\left(2x-1\right)^2+\left(y+1\right)^2\)
8 tháng 11 2017
a) \(\left(2x+y\right)\left(4x^2-2xy+y^2\right)-\left(2x-y\right)\left(4x^2+2xy+y^2\right)\)
\(=8x^3+y^3-8x^3+y^3\)
\(=2y^3\)
b) \(\left(x^2-1\right)^2-\left(x^4+x^2+1\right)\left(x^2-1\right)\)
\(=\left(x^2-1\right)\left(x^2-1-x^4-x^2-1\right)\)
\(=\left(x^2-1\right)\left(-x^4-2\right)\)
\(=-x^6+x^4-2x^2+2\).
13 tháng 10 2017
a. \(x^3+4x^2-31x-70=x^3+2x^2+2x^2+4x-35x-70=\left(x^3+2x^2\right)+\left(2x^2+4x\right)-\left(35x+70\right)=x^2\left(x+2\right)+2x\left(x+2\right)-35\left(x+2\right)=\left(x+2\right)\left(x^2+2x-35\right)=\left(x+2\right)\left(x^2+7x-5x-35\right)=\left(x+2\right)[\left(x^2+7x\right)-\left(5x+35\right)]=\left(x+2\right)\left[x\left(x+7\right)-5\left(x+7\right)\right]=\left(x+2\right)\left(x+7\right)\left(x-5\right)\)
b. \(y^2-y-12=y^2-4y+3y-12=\left(y^2+3y\right)-\left(4y+12\right)=y\left(y+3\right)-4\left(x+3\right)=\left(x+3\right)\left(y-4\right)\)
c. \(x^2-3x^2+4x-2=-2x^2+4x-2=-2\left(x^2-2x+1\right)=-2\left(x-1\right)^2\)
\(y^2-4x^2+4x-1\\ =y^2-\left(4x^2-4x+1\right)\\ =y^2-\left(2x-1\right)^2\\ =\left(y-2x+1\right)\left(y+2x-1\right)\)
y2 - 4x2 + 4x - 1
= y2 - ( 4x2 - 4x + 1)
= y2 - ( 2x - 1 )2
= ( y - 2x + 1 ) . ( y + 2x -1 )