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a, Thay x=-1 vào biểu thức A ta có:
\(A=2\left(-1\right)^2+\left(-1\right)+1\)
\(A=2.1+\left(-1\right)+1\)
\(A=2\)
Thay \(x=\dfrac{1}{4}\) vào biểu thức A ta có:
\(A=2\left(\dfrac{1}{4}\right)^2+\dfrac{1}{4}+1\)
\(A=2.\dfrac{1}{16}+\dfrac{1}{4}+1\)
\(A=\dfrac{1}{8}+\dfrac{1}{4}+1\)
\(A=\dfrac{1}{8}+\dfrac{2}{8}+1\)
\(A=\dfrac{11}{8}\)
b, Thay x=-1; y=3 vào biểu thức B ta có:
\(B=\left(-1\right)^2.3^2+\left(-1\right).3+\left(-1\right)^3+3^3\)
\(B=1.9-3-1+27\)
\(B=2+27\)
\(B=29\)
c, Thay x=-1 vào biểu thức C ta có:
\(C=\left(-1\right)^2+\left(-1\right)^4+\left(-1\right)^6+\left(-1\right)^8+...+\left(-1\right)^{100}\)
\(C=1^4+1^6+1^8+1^9+...+1^{100}\)
\(C=100\)
d, Thay x+y=3; xy=-5 vào biểu thức D ta có:
\(D=3.\left(x+1\right).\left(y+1\right)\)
\(D=3.\left[\left(x.y\right)+1\right]\)
\(D=3.\left[\left(-5\right)+1\right]\)
\(D=3.\left(-4\right)\)
\(D=-12\)
Tích mình nha!!!
Thay x = \(\frac{1}{2}\), y = \(\frac{-1}{3}\)vào biểu thức A
Ta được: \(A=3.\left(\frac{1}{2}\right)^3.\left(\frac{-1}{3}\right)+6.\left(\frac{1}{2}\right)^2.\left(-\frac{1}{3}\right)^2+3.\frac{1}{2}.\left(\frac{-1}{3}\right)^2\)
\(=\frac{3.1.\left(-1\right)}{8.3}+\frac{6.1.1}{4.9}+\frac{3.1.1}{2.9}\)
\(=\frac{-1}{8}+\frac{1}{6}+\frac{1}{6}=\frac{5}{24}\)
Thay x = -1, y = 3 vào biểu thức B
Ta được:
B = (-1)2. 32 + (-1) . 3 +(-1)3 +33
= 9 + (-3) + (-1) + 27
= 32
\(A=3x^2y+6x^2y^2+3xy^2\)
\(A=3\left(\frac{1}{2}\right)^3\left(-\frac{1}{3}\right)+6\left(\frac{1}{2}\right)^2\left(-\frac{1}{3}\right)^2+3\left(\frac{1}{2}\right)\left(-\frac{1}{3}\right)^2\)
\(A=\left(-\frac{1}{8}\right)+\frac{1}{6}+\frac{1}{6}\)
\(A=\frac{5}{24}\)
Vậy: Biểu thức A tại x = 1/2; y = -1/3 là: 5/24
\(B=x^2y^2+xy+x^3+y^3\)
\(B=\left(-1\right)^2.3^2+\left(-1\right).3+\left(-1\right)^3+3^3\)
\(B=9+\left(-3\right)+26\)
\(B=32\)
Vậy: biểu thức B tại x = -1; y = 3 là: 32
a/ Thay: \(x=\frac{1}{2};y=-\frac{1}{3}\) vào A ta có:
A = 3x3y + 6x2y2 + 3xy3
A = \(3.\left(\frac{1}{2}\right)^3.\left(-\frac{1}{3}\right)+6.\left(\frac{1}{2}\right)^2.\left(-\frac{1}{3}\right)^2+3.\frac{1}{2}.\left(-\frac{1}{3}\right)^3\)
A = \(3.\frac{1}{8}.\left(-\frac{1}{3}\right)+6.\frac{1}{4}.\frac{1}{9}+3.\frac{1}{2}.\frac{1}{27}\)
A = \(-\frac{1}{8}+\frac{1}{6}+\frac{1}{18}\)
A = \(\frac{7}{72}\)
b/ Thay \(x=-1;y=3\) vào B ta có:
B = x2y2 +xy + x3 + y3
B = \(\left(-1\right)^2.3^2+\left(-1\right).3+\left(-1\right)^3+3^3\)
B = \(1.9+\left(-3\right)+\left(-1\right)+27\)
B = 32
a) A= -1/72
b) B= 32
Sorry vì ko bấm phân số được. Vote cho mình nha :3
1.
\(-3x^5y^4+3x^2y^3-7x^2y^3+5x^5y^4\)
\(=(-3x^5y^4+5x^5y^4)+(3x^2y^3-7x^2y^3)\)
\(=2x^5y^4-4x^2y^3\)
2.
\(\frac{1}{2}x^4y-\frac{3}{2}x^3y^4+\frac{5}{3}x^4y-x^3y^4\)
\(=(\frac{1}{2}x^4y+\frac{5}{3}x^4y)-(\frac{3}{2}x^3y^4+x^3y^4)\)
\(=\frac{13}{6}x^4y-\frac{5}{2}x^3y^4\)
3.
\(5x-7xy^2+3x-\frac{1}{2}xy^2\)
\(=(5x+3x)-(7xy^2+\frac{1}{2}xy^2)\)
\(=8x-\frac{15}{2}xy^2\)
4.
\(\frac{-1}{5}x^4y^3+\frac{3}{4}x^2y-\frac{1}{2}x^2y+x^4y^3\)
\(=(\frac{-1}{5}x^4y^3+x^4y^3)+(\frac{3}{4}x^2y-\frac{1}{2}x^2y)\)
\(=\frac{4}{5}x^4y^3+\frac{1}{4}x^2y\)
5.
\(\frac{7}{4}x^5y^7-\frac{3}{2}x^2y^6+\frac{1}{5}x^5y^7+\frac{2}{3}x^2y^6\)
\(=(\frac{7}{4}x^5y^7+\frac{1}{5}x^5y^7)+(-\frac{3}{2}x^2y^6+\frac{2}{3}x^2y^6)\)
\(=\frac{39}{20}x^5y^7-\frac{5}{6}x^2y^6\)
6.
\(\frac{1}{3}x^2y^5(-\frac{3}{5}x^3y)+x^5y^6=(\frac{1}{3}.\frac{-3}{5})(x^2.x^3)(y^5.y)+x^5y^6\)
\(=\frac{-1}{5}x^5y^6+x^5y^6=\frac{4}{5}x^5y^6\)
1, \(\left(xy\right)^2-\frac{1}{2}x^2y^2+3xy^2.\left(-\frac{1}{3}x\right)\)
\(=x^2y^2-\frac{1}{2}x^2y^2-x^2y^2\)
\(=-\frac{1}{2}x^2y^2\)
2, \(4.\left(-\frac{1}{2}x\right)^2-\frac{3}{2}x.\left(-x\right)+\frac{1}{3}x^2\)
\(=x^2+\frac{3}{2}x^2+\frac{1}{3}x^2\)
\(=\frac{17}{6}x^2\)
3, \(-4.\left(2x\right)^2y^3+\frac{1}{2}xy.\left(-2xy^2\right)+\frac{1}{4}x^2y^3\)
\(=-16x^2y^3-x^2y^3+\frac{1}{4}x^2y^3\)
\(=-\frac{67}{4}x^2y^3\)
4, \(\frac{1}{3}x^4y-\frac{5}{3}x^3.\left(\frac{5}{2}xy\right)+\frac{3}{4}x^4y\)
\(=\frac{1}{3}x^4y-\frac{25}{6}x^4y+\frac{3}{5}x^4y\)
\(=-\frac{97}{30}x^4y\)
5, \(\left(-2x^3y^4\right)^2-5x^2y.\left(\frac{3}{4}x^4y^7\right)-\frac{2}{3}x^6y^8\)
\(=4x^6y^8-\frac{15}{4}x^6y^8-\frac{2}{3}x^6y^8\)
\(=-\frac{5}{12}x^6y^8\)
a: \(A=3x^2y^3-5x^2+3x^3y^2\)
\(B=x^2y^3+\dfrac{5}{2}x^5y-5x^2y\)
b: \(A+B=4x^2y^3+5x^2+\dfrac{5}{2}x^5y+3x^3y^2-5x^2y\)
\(A-B=2x^2y^3-5x^2+3x^3y^2-\dfrac{5}{2}x^5y+5x^2y\)
c: Khi x=-1 và y=-1/3 thì \(A=3\cdot\left(-1\right)^2\cdot\dfrac{-1}{27}-5\cdot\left(-1\right)^2+3\cdot\left(-1\right)^3\cdot\dfrac{1}{9}\)
\(=-\dfrac{1}{9}-5-\dfrac{1}{3}=\dfrac{-49}{9}\)
I . Trắc Nghiệm
1B . 2D . 3C . 5A
II . Tự luận
2,a,Ta có: A+(x\(^2\)y-2xy\(^2\)+5xy+1)=-2x\(^2\)y+xy\(^2\)-xy-1
\(\Leftrightarrow\) A=(-2x\(^2\)y+xy\(^2\)-xy-1) - (x\(^2\)y-2xy\(^2\)+5xy+1)
=-2x\(^2\)y+xy\(^2\)-xy-1 - x\(^2\)y+2xy\(^2\)-5xy-1
=(-2x\(^2\)y - x\(^2\)y) + (xy\(^2\)+ 2xy\(^2\)) + (-xy - 5xy ) + (-1 - 1)
= -3x\(^2\)y + 3xy\(^2\) - 6xy - 2
b, thay x=1,y=2 vào đa thức A
Ta có A= -3x\(^2\)y + 3xy\(^2\) - 6xy - 2
= -3 . 1\(^2\) . 2 + 3 .1 . 2\(^2\) - 6 . 1 . 2 -2
= -6 + 12 - 12 - 2
= -8
3,Sắp xếp
f(x) =9-x\(^5\)+4x-2x\(^3\)+x\(^2\)-7x\(^4\)
=9-x\(^5\)-7x\(^4\)-2x\(^3\)+x\(^2\)+4x
g(x) = x\(^5\)-9+2x\(^2\)+7x\(^4\)+2x\(^3\)-3x
=-9+x\(^5\)+7x\(^4\)+2x\(^3\)+2x\(^2\)-3x
b,f(x) + g(x)=(9-x\(^5\)-7x\(^4\)-2x\(^3\)+x\(^2\)+4x) + (-9+x\(^5\)+7x\(^4\)+2x\(^3\)+2x\(^2\)-3x)
=9-x\(^5\)-7x\(^4\)-2x\(^3\)+x\(^2\)+4x-9+x\(^5\)+7x\(^4\)+2x\(^3\)+2x\(^2\)-3x
=(9-9)+(-x\(^5\)+x\(^5\))+(-7x\(^4\)+7x\(^4\))+(-2x\(^3\)+2x\(^3\))+(x\(^2\)+2x\(^2\))+(4x-3x)
= 3x\(^2\) + x
g(x)-f(x)=(-9+x\(^5\)+7x\(^4\)+2x\(^3\)+2x\(^2\)-3x) - (9-x\(^5\)-7x\(^4\)-2x\(^3\)+x\(^2\)+4x)
=-9+x\(^5\)+7x\(^4\)+2x\(^3\)+2x\(^2\)-3x-9+x\(^5\)+7x\(^4\)+2x \(^3\)-x\(^2\)-4x
=(-9-9)+(x\(^5\)+x\(^5\))+(7x\(^4\)+7x\(^4\))+(2x\(^3\)+2x\(^3\))+(2x\(^2\)-x\(^2\))+(3x-4x)
= -18 + 2x\(^5\) + 14x\(^4\) + 4x\(^3\) + x\(^2\) - x
thay x=-1;y=3 vào biểu thức B ta đc
B=(-1)2.32+(-1).3+(-1)2+32
B=9+(-3)+(-1)+9
B=14
b/ Tại \(x=-1;y=3\) ta có
B= \(\left(-1\right)^2.\left(3\right)^2+\left(-1\right).3+\left(-1\right)^3+\left(3\right)^3\)
B= \(1.9+\left(-3\right)+\left(-1\right)+27\)
B= \(9+\left(-3\right)+\left(-1\right)+27\)
B= 32