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a) \(x^2-2xy-4z^2+y^2\)
\(\Leftrightarrow\left(x^2-2xy+y^2\right)-\left(2z\right)^2\)
\(\Leftrightarrow\left(x-y\right)^2-\left(2z\right)^2\)
\(\Leftrightarrow\left[\left(x-y\right)+2z\right]\left[\left(x-y\right)-2z\right]\)
\(\Leftrightarrow\left(x-y+2z\right)\left(x-y-2z\right)\)
Tại x=6, y=-4, z=45
\(\left[6-\left(-4\right)+2.45\right]\left[6-\left(-4\right)-2.45\right]=100.\left(-80\right)=-8000\)
b) \(3\left(x-3\right)\left(x+7\right)+\left(x-4\right)^2+48\)
\(\Leftrightarrow3\left(x^2+7x-3x-21\right)+\left(x^2-4x+4\right)+48\)
\(\Leftrightarrow3x^2+21x-9x-63+x^2-4x+4+48\)
\(\Leftrightarrow4x^2+8x-11\)
Tại x=0,5 ta có:
\(4.\left(0,5\right)^2+8.0,5-11=-6\)
a)Đặt \(A=x^2-2xy-4z^2+y^2\)
\(=\left(x^2-2xy+y^2\right)-\left(2z\right)^2\)
\(=\left(x-y\right)^2-\left(2z\right)^2\)
\(=\left(x-y-2z\right)\left(x-y+2z\right)\)
Thay \(x=6;y=-4;z=45\) vào A, ta có:
\(A=\left[6-\left(-4\right)-2\cdot45\right]\left[6-\left(-4\right)+2\cdot45\right]\)
\(=100\cdot\left(-80\right)\)
\(=-8000\)
Vậy \(A=-8000\)
b) Đặt \(B=3\left(x-3\right)\left(x+7\right)+\left(x-4\right)^2+48\)
\(=3\left(x^2+7x-3x-21\right)+x^2-4x+4+48\)
\(=3x^2+12x-63+x^2-4x+52\)
\(=4x^2+8x-11\)
Thay \(x=0,5\) vào B, ta có:
\(B=4\cdot\left(0,5\right)^2+8\cdot0,5-11\)
\(=1\cdot4-11\)
\(=-6\)
Vậy \(B=-6\)
`a, = 3x^2y - 3xy + 6x^2y + 5xy - 9x^2y`
`= 2xy`.
Thay `x = 2/3; y = -3/4` vào BT:
`2 . 2/3 . -3/4 = -1.`
`b, x(x-2y) - y(y^2-2x)`
`= x^2 - 2xy - y^3 + 2xy`
`= x^2 - y^3`
Thay `x = 5; y =3` vào BT:
`= 5^2 - 3^3 = 25 - 27 = -2`
a) \(3x^2y-\left(3xy-6x^2y\right)+\left(5xy-9x^2y\right)\)
\(=3x^2y-3xy+6x^2y+5xy-9x^2y\)
\(=2xy\)
Thay \(x=\dfrac{2}{3},y=-\dfrac{3}{4}\) vào Bt ta có:
\(2\cdot\dfrac{2}{3}\cdot-\dfrac{3}{4}=-1\)
b) \(x\left(x-2y\right)-y\left(y^2-2x\right)\)
\(=x^2-2xy-y^3+2xy\)
\(=x^2-y^3\)
Thay \(x=5,y=3\) vào Bt ta có:
\(5^2-3^3=-3\)
a) \(x^2-2xy-4z^2+y^2=\left(x-y\right)^2-4z^2=\left(x-y-2z\right)\left(x-y+2z\right)=\left(6+4-2.45\right)\left(6+4+2.45\right)=-8000\)b) \(3\left(x-3\right)\left(x+7\right)+\left(x-4\right)^2+48=3\left(x^2+4x-21\right)+\left(x^2-8x+16\right)+48=4x^2+4x+1=\left(2x+1\right)^2=\left(2.0,5+1\right)^2=4\)
a: Ta có: \(x^2-2xy+y^2-4z^2\)
\(=\left(x-y\right)^2-\left(2z\right)^2\)
\(=\left(x-y-2z\right)\left(x-y+2z\right)\)
\(=\left(6+4-2\cdot45\right)\left(6+4+2\cdot45\right)\)
\(=-8000\)
b: Ta có: \(3\left(x-3\right)\left(x+7\right)+\left(x-4\right)^2+48\)
\(=3\left(x^2+4x-21\right)+\left(x-4\right)^2+48\)
\(=3x^2+12x-63+x^2-8x+16+48\)
\(=2x^2+4x+1\)
\(=2\cdot\dfrac{1}{4}+4\cdot\dfrac{1}{2}+1\)
\(=\dfrac{7}{2}\)
a) \(5x^2-2x\left(3x+\frac{3}{2}\right)=-x^2-3x=-x\left(x+3\right)=-3\left(3+3\right)=-18\)
b) \(3x\left(x-4y\right)-\frac{12}{5}y\left(y-5x\right)=3x^2-\frac{12}{5}y^2=3\left(x^2-\frac{4}{5}y^2\right)\)
\(=3\left(4^2-\frac{4}{5}.5^2\right)=3.\left(-4\right)=-12\)
c) \(\left(x-2\right)^2-\left(x+7\right)\left(x-7\right)=x^2-4x+4-x^2+49=-4x+53=-4.3+53=41\)
d) \(x^2+12x+36=\left(x+6\right)^2=\left(64+6\right)^2=70^2=4900\)
e) \(\left(x-3\right)^2-\left(x-4\right)\left(x+4\right)=x^2-6x+9-x^2+16=-6x+25=-6\left(-1\right)+25\)
= 31
f) \(\left(3x+2y\right)^2-4y\left(3x+y\right)=9x^2+12xy+4y^2-12xy-4y^2=9x^2=9\left(-\frac{1}{3}\right)^2=1\)
a) \(x^2-xy+x-y\)
\(=x\left(x-y\right)+\left(x-y\right)\)
\(=\left(x+1\right)\left(x-y\right)\)
b)\(x^2-2xy+y^2-z^2\)
\(=\left(x^2-2xy+y^2\right)-z^2\)
\(=\left(x-y\right)^2-z^2\)
\(=\left(x-y-z\right)\left(x-y+z\right)\)
c)\(5x-5y+ax-ay\)
\(=5\left(x-y\right)+a\left(x-y\right)\)
\(=\left(5+a\right)\left(x-y\right)\)
d)\(a^3-a^2x-ay+xy\)
\(=a^2\left(a-x\right)-y\left(a-x\right)\)
\(=\left(a^2-y\right)\left(a-x\right)\)
Bài 2 :
a) \(x^2-2xy-47^2+y^2\)
\(=x^2-2xy+y^2-47^2\)
\(=\left(x-y\right)^2-47^2\)
\(=\left(x-y-47\right)\left(x-y+47\right)\)
Bài 1
a) x2 - xy + x - y
= x.(x - y) + (x - y)
= (x - y) . (x + 1)
b) x2 - 2xy + y2 - z2
= (x - y)2 - z2
= (x - y - z) . (x - y + z)
c) 5x - 5y + ax - ay
= 5 . (x - y) + a . (x - y)
= (5 + a ) . (x - y)
d) a3 - a2x - ay + xy
=
a3−a2x−ay+xya3−a2x−ay+xy
=(a3−a2x)−(ay−xy)=(a3−a2x)−(ay−xy)
=a2(a−x)−y(a−x)=a2(a−x)−y(a−x)
=(a2−y)(a−x)
a)x2-2xy-4x2+y2
= (x2-2xy+y2)-(2x)2
= (x-y)2-(2x)2 = (x-y-2x)(x-y+2x)(1)
Thay x=6; y=-4; z=45 ta được:
(1)<=>(6+4-90)(6+4+90)= (10-90).(10+90)=-80.100= -8000
\(a.10x\left(x-y\right)-6y\left(y-x\right)\\ =10x\left(x-y\right)+6y\left(x-y\right)\\ =\left(10x-6y\right)\left(x-y\right)\\ =2\left(5x-3y\right)\left(x-y\right)\)
\(b.14x^2y-21xy^2+28x^3y^2\\ =7xy\left(x-y+xy\right)\)
\(c.x^2-4+\left(x-2\right)^2\\ =\left(x-2\right)\left(x+2\right)+\left(x-2\right)^2\\ =\left(x-2\right)\left(x+2+x-2\right)\\ =2x\left(x-2\right)\)
\(d.\left(x+1\right)^2-25\\ =\left(x+1-5\right)\left(x+1+5\right)=\left(x-4\right)\left(x+6\right)\)
\(A=x^2-2xy-4z^2+y^2\)
\(=\left(x-y\right)^2-\left(2z\right)^2\)
\(=\left(x-y+2z\right)\left(x-y-2z\right)\)
\(=\left(6+4+45\right)\left(6+4-45\right)\)
\(=-1925\)