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`@` `\text {Ans}`
`\downarrow`
`A - B`
`= (x^5y^2 + 7x^2y^4 + 5xy^3 + xy + 2) - (x^2y^4 + 5xy^3 + x^5y^2)`
`= x^5y^2 + 7x^2y^4 + 5xy^3 + xy + 2 - x^2y^4 - 5xy^3 - x^5y^2`
`= (x^5y^2 - x^5y^2) + (7x^2y^4 - x^2y^4) + (5xy^3 - 5xy^3) + xy + 2`
`= 6x^2y^4 + xy + 2`
a, mình nghĩ đề là cm đẳng thức nhé
\(VT=\left(5x^4-3x^3+x^2\right):3x^2=\frac{5x^4}{3x^2}-\frac{3x^3}{3x^2}+\frac{x^2}{3x^2}=\frac{5}{3}x^2-x+\frac{1}{3}=VP\)
Vậy ta có đpcm
b, \(VT=\left(5xy^2+9xy-x^2y^2\right):\left(-xy\right)=\frac{5xy^2}{-xy}+\frac{9xy}{-xy}-\frac{x^2y^2}{-xy}\)
\(=-5y-9+xy=VP\)
Vậy ta có đpcm
c, \(VT=\left(x^3y^3-x^2y^3-x^3y^2\right):x^2y^2=\frac{x^3y^3}{x^2y^2}-\frac{x^2y^3}{x^2y^2}-\frac{x^3y^2}{x^2y^2}=xy-y-x=VP\)
Vậy ta có đpcm
\(a,\dfrac{6x^2y^2}{8xy^5}=\dfrac{2x}{4y^3}\)
\(b,\dfrac{x^2-xy}{5xy-5y^2}=\dfrac{x\left(x-y\right)}{5y\left(x-y\right)}\)
\(c,\dfrac{x^3-x}{3x+3}=\dfrac{x\left(x^2-1\right)}{3\left(x^2+1\right)}=\dfrac{x\left(x-1\right)\left(x+1\right)}{3\left(x+1\right)}=\dfrac{x\left(x-1\right)}{3}\)
a) \(\dfrac{6x^2y^2}{8xy^5}=\dfrac{3x}{4y^3}\)
b) \(\dfrac{x^2-xy}{5xy-5y^2}=\dfrac{x\left(x-y\right)}{5y\left(x-y\right)}=\dfrac{x}{5y}\)
c) \(\dfrac{x^3-x}{3x+3}=\dfrac{x\left(x^2-1\right)}{3\left(x+1\right)}=\dfrac{x\left(x+1\right)\left(x-1\right)}{3\left(x+1\right)}=\dfrac{x\left(x-1\right)}{3}\)
d. \(\left(x-3y\right)\left(3x^2+y^2+5xy\right)\)
\(=3x^3+xy^2+5x^2y-9x^2y-3y^3-15xy^2\)
\(=3x^3-14xy^2-4x^2y-3y^3\)
Bài 2:
a. \(x^2-y^2-5x+5y\)
\(=\left(x-y\right)\left(x+y\right)-5\left(x-y\right)\)
\(=\left(x+y-5\right)\left(x-y\right)\)
b. \(x^3-x^2-4x^2+8x-4\)
\(=x^2\left(x-1\right)-4\left(x^2-2x+1\right)\)
\(=x^2\left(x-1\right)-4\left(x-1\right)^2\)
\(=\left(x-1\right)\left[x^2-4\left(x-1\right)\right]\)
\(=\left(x-1\right)\left(x^2-4x+4\right)\)
\(=\left(x-1\right)\left(x-2\right)^2\)
Bài 3:
\(87^2+26.87+13^2\)
\(=\left(87+ 13\right)^2\)
\(=100^2\)
\(=10000\)
Bài 1:
a. \(3x^2\left(5x^2-4x+3\right)\)
\(=15x^4-12x^3+9x^2\)
b. \(-5xy\left(3x^2y-5xy-y^2\right)\)
\(=-15x^3y^2+25x^2y^2+5xy^3\)
c. \(\left(5x^2-4x\right)\left(x-3\right)\)
\(=5x^3-19x^2-4x^2+12x\)
Làm tính nhân
(4x3+3xy2-2y3).(3x2-5xy-6y2)
=12x5+12y5-20x4y-36x2y3-8xy4
Phân tích đa thức thành nhân tử
10x3+5x2y-10x2y-10xy2+5y3
=10x3-5x2y-10xy2+5y3
=5(2x3-x2y-2xy2+y3-)
Câu 2 nha
\(a,x^4+2x^3+x^2\)
\(=x^2\left(x^2+2x+1\right)\)
\(=x^2\left(x+1\right)^2\)
\(c,x^2-x+3x^2y+3xy^2+y^3-y\)
\(=\left(x^3+3x^2y+3xy^2+y^3\right)-\left(x+y\right)\)
\(=\left(x+y\right)^3-\left(x+y\right)\)
\(=\left(x+y\right)\left(x^2+2xy+y^2-1\right)\)
Ta có :
\(\frac{6x^2y^2}{8xy^5}=\frac{3x}{4y^3}\)
\(\frac{x^2-xy}{5xy-5y^2}=\frac{x\left(x-y\right)}{5y\left(x-y\right)}=\frac{x}{5y}\)
Hok tốt !
Lời giải:
a) \(\frac{45x(3-x)}{15(x-3)^3}=\frac{-45x(x-3)}{15(x-3)^3}=\frac{-3x}{(x-3)^2}\)
b) \(\frac{36(x-2)^3}{32-16x}=\frac{36(x-2)^3}{-16(x-2)}=\frac{-9}{4}(x-2)^2\)
c) \(\frac{x^2-xy}{5y^2-5xy}=\frac{x(x-y)}{-5y(x-y)}=\frac{x}{-5y}\)
d) \(\frac{y^2-x^2}{x^3-3x^2y+3xy^2-y^3}=\frac{-(x^2-y^2)}{(x-y)^3}=\frac{-(x-y)(x+y)}{(x-y)^3}=\frac{-(x+y)}{(x-y)^2}\)
Bài 1:
a) \(\dfrac{16-\left(x+3\right)^2}{x^2-2x+1}\)
\(=\dfrac{\left(4-x-3\right)\left(4+x+3\right)}{\left(x-1\right)^2}\)
\(=\dfrac{\left(1-x\right)\left(x+7\right)}{\left(1-x\right)^2}\)
\(=\dfrac{x+7}{1-x}\)
b) \(\dfrac{x^2+4x+4}{x^2+5x+6}\)
\(=\dfrac{\left(x+2\right)^2}{x^2+2x+3x+6}\)
\(=\dfrac{\left(x+2\right)^2}{x\left(x+2\right)+3\left(x+2\right)}\)
\(=\dfrac{\left(x+2\right)^2}{\left(x+2\right)\left(x+3\right)}\)
\(=\dfrac{x+2}{x+3}\)
Bài 2:
a) \(\dfrac{3xy+6}{6xy+12}\)
\(=\dfrac{3\left(xy+2\right)}{6\left(xy+2\right)}\)
\(=\dfrac{3}{6}\)
\(=\dfrac{1}{2}\left(Đpcm\right)\)
b) \(\dfrac{x^2-xy}{5y^2-5xy}\)
\(=\dfrac{x\left(x-y\right)}{5y\left(y-x\right)}\)
\(=\dfrac{-x\left(y-x\right)}{5y\left(y-x\right)}\)
\(=-\dfrac{x}{5y}\)
Chỗ này hình như ghi sai đề
\(A+B\\ =x^5y^2+7x^2y^4+5xy^3+xy+2+x^2y^4+5xy^3+x^5y^2\\ =\left(x^5y^2+x^5y^2\right)+\left(7x^2y^4+x^2y^4\right)+\left(5xy^3+5xy^3\right)+xy+2\\ =2x^5y^2+8x^2y^4+10xy^3+xy+2\)
`@` `\text {Ans}`
`\downarrow`
`A + B`
`= (x^5y^2 + 7x^2y^4 + 5xy^3 + xy + 2) + (x^2y^4 + 5xy^3 + x^5y^2)`
`= x^5y^2 + 7x^2y^4 + 5xy^3 + xy + 2 + x^2y^4 + 5xy^3 + x^5y^2`
`= (x^5y^2 + x^5y^2) + (7x^2y^4+ x^2y^4) + (5xy^3+ 5xy^3) + xy + 2`
`= 2x^5y^2 + 8x^2y^4 + 10xy^3 + xy + 2`