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17 tháng 12 2023
a: \(M=2\left(x+5\right)^2+5\left(x-2\right)^2-7\left(x+3\right)\left(x-3\right)\)
\(=2\left(x^2+10x+25\right)+5\left(x^2-4x+4\right)-7\left(x^2-9\right)\)
\(=2x^2+20x+50+5x^2-20x+20-7x^2+63\)
\(=113\)
b: \(H=\left(2x-3y\right)^2-\left(3y-2\right)\left(3y+2\right)-\left(1-2x\right)^2+4x\left(3y-1\right)\)
\(=4x^2-12xy+9y^2+12xy-4x-\left(9y^2-4\right)-\left(4x^2-4x+1\right)\)
\(=4x^2+9y^2-4x-9y^2+4-4x^2+4x-1\)
=3
c: \(N=\left(2x+3y\right)^2+\left(3x-2y\right)^2-13\left(x+y\right)\left(x-y\right)-26\left(y+1\right)\left(y-1\right)\)
\(=4x^2+12xy+9y^2+9x^2-12xy+4y^2-13\left(x^2-y^2\right)-26\left(y^2-1\right)\)
\(=13x^2+13y^2-13x^2+13y^2-26y^2+26\)
=26
d: \(K=\left(x^2y-3\right)^2-\left(2x-y\right)^3+xy^2\left(6-x^3\right)+8x^3-6x^2y-y^3\)
\(=x^4y^2-6x^2y+9+6xy^2-x^4y^2+8x^3-6x^2y-y^3-\left(2x-y\right)^3\)
\(=-12x^2y+9-y^3+6xy^2+8x^3-\left(8x^3-12x^2y+6xy^2-y^3\right)\)
\(=\left(8x^3-12x^2y+6xy^2-y^3\right)-\left(8x^3-12x^2y+6xy^2-y^3\right)+9\)
=9
e: \(P=\left(4x+3\right)\left(16x^2-12x+9\right)-\left(-23+64x^3\right)\)
\(=\left(4x\right)^3+3^3+23-64x^3\)
\(=64x^3+27+23-64x^3\)
=50
h: \(Q=\left(x+5y\right)\left(x^2-5xy+25y^2\right)+\left(x-5y\right)\left(x^2+5xy+25y^2\right)-\dfrac{1}{2}\left(4x^3-7\right)\)
\(=x^3+125y^3+x^3-125y^3-2x^3+\dfrac{7}{2}\)
=7/2
AP
3
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giúp tui với tui đang cần gấp ạ xong tui tick
11
HQ
Hà Quang Minh
Giáo viên
1 tháng 8 2023
Bài 1:
\(a,x^2-y^2-2x+2y=\left(x-y\right)\left(x+y\right)-2\left(x-y\right)=\left(x-y\right)\left(x+y-2\right)\)
\(b,2x+2y-x^2-xy=2\left(x+y\right)-x\left(x+y\right)=\left(2-x\right)\left(x+y\right)\)
\(c,3a^2-6ab+3b^2-12c^2=3\left(a-b\right)^2-12c^2=3\left[\left(a-b\right)^2-4c^2\right]=3\left(a-b-2c\right)\left(a-b+2c\right)\)
\(d,x^2-25+y^2+2xy=\left(x-y\right)^2-25=\left(x-y-5\right)\left(x-y+5\right)\)
HQ
Hà Quang Minh
Giáo viên
1 tháng 8 2023
Bài 1:
\(e,a^2+2ab+b^2-ac-bc=\left(a+b\right)^2-c\left(a+b\right)=\left(a+b-c\right)\left(a+b\right)\)
\(f,x^2-2x-4y^2-4y=\left(x-1\right)^2-\left(2y+1\right)^2=\left(x-2y-2\right)\left(x+2y\right)\)
\(g,x^2y-x^3-9y+9x=x^2\left(y-x\right)-9\left(y-x\right)=\left(x-3\right)\left(x+3\right)\left(y-x\right)\)
\(h,x^2\left(x-1\right)+16\left(1-x\right)=\left(x-1\right)\left(x-4\right)\left(x+4\right)\)
Tui đang cần gấp ai giúp tui với xogn tui tick
KV
18 tháng 7 2023
1) \(\left(x+\dfrac{1}{3}\right)^3=x^3+3.x^2.\dfrac{1}{3}+3.x.\left(\dfrac{1}{3}\right)^2+\left(\dfrac{1}{3}\right)^3\)
\(=x^3+x^2+\dfrac{x}{3}+\dfrac{1}{27}\)
2) \(\left(2x+y^2\right)^3=\left(2x\right)^3+3.\left(2x\right)^2.y^2+3.2x.\left(y^2\right)^2+\left(y^2\right)^3\)
\(=8x^3+12x^2y^2+6xy^4+y^6\)
3) \(\left(\dfrac{1}{2}x^2+\dfrac{1}{3}y\right)^3=\left(\dfrac{1}{2}x^2\right)^3+3.\left(\dfrac{1}{2}x^2\right)^2.\dfrac{1}{3}y+3.\dfrac{1}{2}x^2.\left(\dfrac{1}{3}y\right)^2+\left(\dfrac{1}{3}y\right)^3\)
\(=\dfrac{1}{8}x^6+\dfrac{1}{4}x^4y+\dfrac{1}{6}x^2y^2+\dfrac{1}{27}y^3\)
4) \(\left(3x^2-2y\right)^3=\left(3x^2\right)^3-3.\left(3x^2\right)^2.2y+3.3x^2.\left(2y\right)^2-\left(2y\right)^3\)
\(=27x^6-54x^4y+36x^2y^2-8y^3\)
5) \(\left(\dfrac{2}{3}x^2-\dfrac{1}{2}y\right)^3=\left(\dfrac{2}{3}x^2\right)^3-3.\left(\dfrac{2}{3}x^2\right)^2.\dfrac{1}{2}y+3.\dfrac{2}{3}x^2.\left(\dfrac{1}{2}y\right)^2-\left(\dfrac{1}{2}y\right)^3\)
\(=\dfrac{8}{27}x^6-\dfrac{1}{3}x^4y+\dfrac{1}{2}x^2y^2-\dfrac{1}{8}y^3\)
6) \(\left(2x+\dfrac{1}{2}\right)^3=\left(2x\right)^3+3.\left(2x\right)^2.\dfrac{1}{2}+3.2x.\left(\dfrac{1}{2}\right)^2+\left(\dfrac{1}{2}\right)^3\)
\(=8x^3+6x^2+\dfrac{3}{2}x+\dfrac{1}{8}\)
7) \(\left(x-3\right)^3=x^3-3.x^2.3+3.x.3^2-3^3\)
\(=x^3-9x^2+27x-27\)
KV
18 tháng 7 2023
8) \(\left(x+1\right)\left(x^2-x+1\right)\)
\(=\left(x+1\right)\left(x^2-x.1+1^2\right)\)
\(=x^3+1^3\)
\(=x+1\)
9) \(\left(x-3\right)\left(x^2+3x+9\right)\)
\(=\left(x-3\right)\left(x^2+x.3+3^2\right)\)
\(=x^3-3^3\)
\(=x^3-27\)
10) \(\left(x-2\right)\left(x^2+2x+4\right)\)
\(=\left(x-2\right)\left(x^2+x.2+2^2\right)\)
\(=x^3-2^3\)
\(=x^3-8\)
11) \(\left(x+4\right)\left(x^2-4x+16\right)\)
\(=\left(x+4\right)\left(x^2-x.4+4^2\right)\)
\(=x^3+4^3\)
\(=x^3+64\)
12) \(\left(x-3y\right)\left(x^2+3xy+9y^2\right)\)
\(=\left(x-3y\right)\left[x^2+x.3y+\left(3y\right)^2\right]\)
\(=x^3-\left(3y\right)^3\)
\(=x^3-27y^3\)
13) \(\left(x^2-\dfrac{1}{3}\right)\left(x^4+\dfrac{1}{3}x^2+\dfrac{1}{9}\right)\)
\(=\left(x^2-\dfrac{1}{3}\right)\left[\left(x^2\right)^2+x^2.\dfrac{1}{3}+\left(\dfrac{1}{3}\right)^2\right]\)
\(=\left(x^2\right)^3-\left(\dfrac{1}{3}\right)^3\)
\(=x^6-\dfrac{1}{27}\)
14) \(\left(\dfrac{1}{3}x+2y\right)\left(\dfrac{1}{9}x^2-\dfrac{2}{3}xy+4y^2\right)\)
\(=\left(\dfrac{1}{3}x+2y\right)\left[\left(\dfrac{1}{3}x\right)^2-\dfrac{1}{3}x.2y+\left(2y\right)^2\right]\)
\(=\left(\dfrac{1}{3}x\right)^3+\left(2y\right)^3\)
\(=\dfrac{1}{27}x^3+8y^3\)
5 tháng 4 2022
a: \(\Leftrightarrow2x\left(x+2\right)+4>x^2+4x+4\)
\(\Leftrightarrow2x^2+4x-x^2-4x>0\)
=>x<>0
b: \(\Leftrightarrow3\left(1-2x\right)-24x< 4\left(1-5x\right)\)
=>3-6x-24x<4-20x
=>-30x+3<4-20x
=>-10x<1
hay x>-1/10
c: \(\Leftrightarrow x^2+6x+8>x^2+10x+16+26\)
=>6x+8>10x+42
=>-4x>34
hay x<-17/2
AV
1
26 tháng 7 2023
3:
a: \(M=x+2x-4y-y-3=3x-5y-3\)
bậc là 1
b: \(N=-x^2t+13t^3+xt^2+5t^3-4\)
bậc là 3
5:
S=(3x+4y)*2*2z=4z(3x+4y)
V=3x*4y*2z=24xyz
Khi x=4;y=2;z=1 thì S=4*1*(3*4+4*2)=4*20=80cm2
V=24*4*2*1=192cm3
(2x+3y)2=2x2+12xy+3y2
(5x-y)2=25x2-10xy+y2
(x+1/4)2=x2+1/2x+1/16
(1/3x-1/2y)2=1/9x2-1/3xy+1/4y2
(3x+1)(3x-1)=3x2-1
(x2+2/5y)(x2-2/5y)=x4-4/25y2