Kquả của phép nhân 2xy(3x^2+4x-3y)là: A. 5x^3y+6x^2y-5xy^2 B.5x^3y+6x^2y+5xy^2 C.6x^3y+8x^2y-6xy^2 D.6x^3y+8x^2y+6xy^2
BT11: Tìm hiệu A-B biết
\(a,-x^2y+A+2xy^2-B=3x^2y-4xy^2\)
\(b,5xy^2-A-6yx^2+B=-7xy^2+8x^2y\)
\(c,3x^2y^3-A-5x^3y^2+B=8x^2y^3-4x^3y\)
\(d,-6x^2y^3+A-3x^3y^2-B=2x^2y^3-7x^3y\)
\(e,A-\dfrac{3}{8}xy^2-B+\dfrac{5}{6}x^2y=\dfrac{3}{4}x^2y-\dfrac{5}{8}xy^2\)
\(f,5xy^3-A-\dfrac{5}{8}yx^3+B=\dfrac{21}{4}xy^3-\dfrac{7}{6}x^3y\)
a: =>A-B=3x^2y-4xy^2+x^2y-2xy^2=4x^2y-6xy^2
b: =>B-A=-7xy^2+8x^2y-5xy^2+6x^2y=-12xy^2+14x^2y
=>A-B=12xy^2-14x^2y
c: =>B-A=8x^2y^3-4x^3y-3x^2y^3+5x^3y^2=5x^2y^3+x^3y^2
=>A-B=-5x^2y^3-x^3y^2
d: =>A-B=2x^2y^3-7x^3y+6x^2y^3+3x^3y^2=8x^2y^3-7x^3y+3x^3y^2
a,(3+1)(x-1)
b,5x(3x-2)
c,3x^2y+6xy^2-9xy):3xy
d,(3x^4-6x^3+4x^2):2x^y
e,(8x^4y^3-4x^3y^2+x^2y^2):2x^2y^2
Xác định các đơn thức thu gọn A,B,C,D, cho biết A và C đồng dạng biết:
3x^2y^3-A-5x^3y^2+B=8x^2y^3-4x^3y^2 và -6x^2y^2+C-3x^3y^2-D=2x^2y^3-7x^3y^2
a,\(\dfrac{x+1}{x-3}+\dfrac{-2x^2+2x}{x^2-9}+\dfrac{x-1}{x+3}\)
b,\(\dfrac{1-2x}{6x^3y}+\dfrac{3+2y}{6x^3y}+\dfrac{2x-4}{6x^3y}\)
c,\(\dfrac{5}{2x^2y}+\dfrac{3}{5xy^2}+\dfrac{x}{3y^3}\)
d,\(\dfrac{5}{4\left(x+2\right)}+\dfrac{8-x}{4x^2+8x}\)
c,\(\dfrac{x^2+2}{x^3+1}+\dfrac{2}{x^2+x+1}+\dfrac{1}{1-x}\)
\(a,=\dfrac{x^2+4x+3-2x^2+2x+x^2-4x+3}{\left(x-3\right)\left(x+3\right)}=\dfrac{2\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}=\dfrac{2}{x-3}\\ b,=\dfrac{1-2x+3+2y+2x-4}{6x^3y}=\dfrac{2y}{6x^3y}=\dfrac{1}{x^2}\\ c,=\dfrac{75y^2+18xy+10x^2}{30x^2y^3}\\ d,=\dfrac{5x+8-x}{4x\left(x+2\right)}=\dfrac{4\left(x+2\right)}{4x\left(x+2\right)}=\dfrac{1}{x}\\ c,=\dfrac{x^2+2+2x-2-x^2-x-1}{\left(x-1\right)\left(x^2+x+1\right)}=\dfrac{x-1}{\left(x-1\right)\left(x^2+x+1\right)}=\dfrac{1}{x^2+x+1}\)
Tìm các đơn thức thu gọn A, B, C, D biết A và C đồng dạng đồng thời thỏa mãn các điều kiện sau:
\(3x^2y^3-A-5x^3y^2+B=8x^2y^3-4x^3y^2\) và \(-6x^2y^3+C-3x^3y^2-D=2x^2y^3-7x^3y^2\) nhờ mn giúp mình với
\(3x^2y^3-A-5x^3y^2+B=8x^2y^3-4x^3y^2\)
\(\Leftrightarrow-A+B=5x^2y^3+x^3y^2\)
\(-6x^2y^3+C-3x^3y^2-D=2x^2y^3-7x^3y^2\)
\(\Leftrightarrow C-D=8x^2y^3-4x^3y^2\)
Do \(A\) và \(C\) đồng dạng nên \(A=-5x^2y^3,C=8x^2y^3\) suy ra \(B=x^3y^2,D=4x^3y^2\) hoặc \(A=-x^3y^2,C=-4x^3y^2\) suy ra \(B=5x^2y^3,D=-8x^2y^3\).
Phân tích đa thức sau thành nhân tử
9y^3-y
8y^3-2y(1-2y)^2
2x^3-8x^2+8x
2x^4-6x^3+6x^2-2x
x^3-6x^2y+9xy^2-x
5x^4-15x^3y+15x^2y^2-5xy^3-5x
3x^2+3xy-x-y
6xy-x^2-y^2+25
7m-7n-m^2+2mn-n^2
3xy-3xz+2xyz-xy^2-xz^2
a)\(9y^3-y\)
\(=y\left(9y^2-1\right)\)
\(=y\left(3y-1\right)\left(3y+1\right)\)
\(9y^3-y=y\left(9y^2-1\right)=y\left(3y+1\right)\left(3y-1\right)\)
\(8y^3-2y\left(1-2y\right)^2=2y\left[\left(2y\right)^2-\left(1-2y\right)^2\right]=2y\left(4y-1\right)\)
\(2x^3-8x^2+8x=2x\left(x^2-4x+4\right)=2x\left(x-2\right)^2\)
\(2x^4-6x^3+6x^2-2x=2x\left(x^3-3x^2+3x-1\right)=2x\left(x-1\right)^3\)\(x^3-8x^2+8x=x\left(x^2-8x+8\right)\)
\(5x^4-15x^3y+15x^2y^2-5xy^3-5x=5x\left(x^3-3x^2y+3xy^2-y^3-1\right)=5x\left[\left(x-y\right)^3-1\right]=5x\left(x-y-1\right)\left(x^2-2xy+y^2+x-y+1\right)\)
a)(-6x^3y^4+4x^4y^3):2x^3y^3. b)(5x^4y^2-x^3y^2):x^3y^2. c)(27x^3y^5+9x^2y^4-6x^3y^3):(-3x^2y^3)
a: \(\dfrac{-6x^3y^4+4x^4y^3}{2x^3y^3}\)
\(=\dfrac{-6x^3y^4}{2x^3y^3}+\dfrac{4x^4y^3}{2x^3y^3}\)
\(=-3y+2x\)
b: \(\dfrac{5x^4y^2-x^3y^2}{x^3y^2}=\dfrac{5x^4y^2}{x^3y^2}-\dfrac{x^3y^2}{x^3y^2}\)
\(=5x-1\)
c: \(\dfrac{27x^3y^5+9x^2y^4-6x^3y^3}{-3x^2y^3}\)
\(=-\dfrac{27x^3y^5}{3x^2y^3}-\dfrac{9x^2y^4}{3x^2y^3}+\dfrac{6x^3y^3}{3x^2y^3}\)
\(=-9xy^2-3y+2x\)
a) \(\dfrac{-6x^3y^4+4x^4y^3}{2x^3y^3}\)
\(=\dfrac{2x^3y^3\cdot\left(-3y+2x\right)}{2x^3y^3}\)
\(=-3y+2x\)
\(=2x-3y\)
b) \(\dfrac{5x^4y^2-x^3y^2}{x^3y^2}\)
\(=\dfrac{5x\cdot x^3y^2-x^3y^2\cdot1}{x^3y^2}\)
\(=\dfrac{x^3y^2\cdot\left(5x-1\right)}{x^3y^2}\)
\(=5x-1\)
c) \(\dfrac{27x^3y^5+9x^2y^4-6x^3y^3}{-3x^2y^3}\)
\(=\dfrac{-3x^2y^3\cdot-9xy^2+-3x^2y^3\cdot-3y+-3x^2y^3\cdot2x}{-3x^2y^3}\)
\(=\dfrac{-3x^2y^3\cdot\left(-9xy^2-3y+2x\right)}{-3x^2y^3}\)
\(=-9xy^2-3x+2x\)
a,4xy^2-3x^2y+2x^y2+3x^2y b,1/5xy+4/3xy^-2/5xy^+1/3xy c,3/4x^3y^-2/5xy^+2/5x^3y^+3/5x^3y^2 d,(-4/9xy^).(3/2xy^3)
giúp em nhanh với ạ làm ơn :(
a: \(=\left(4xy^2+2xy^2\right)+\left(3x^2y-3x^2y\right)=6xy^2\)
b: \(=xy\left(\dfrac{1}{5}+\dfrac{1}{3}\right)+xy^2\left(\dfrac{4}{3}-\dfrac{2}{5}\right)=\dfrac{8}{15}xy+\dfrac{14}{15}xy^2\)
d: \(=\dfrac{-4}{9}\cdot\dfrac{3}{2}\cdot xy^2\cdot xy^3=-\dfrac{2}{3}x^2y^5\)
Bài 1: Thực hiện phép tính
a) (x-4) (x+4) - (5-x) (x+1)
b) (3x^2 - 2xy + 4) + ( 5xy - 6x^2 - 7)
Bài 2: Rút gọn biểu thức
a) 3x^2 (2x + y) - 2y(4x^2 - y)
b) (x+3y) (x-2y) - (x^4 - 6x^2y^3): x^2y
Bài 1:
a, (\(x\) - 4).(\(x\) + 4) - (5 - \(x\)).(\(x\) + 1)
= \(x^2\) - 16 - 5\(x\) - 5 + \(x^2\) + \(x\)
= (\(x^2\) + \(x^2\)) - (5\(x\) - \(x\)) - (16 + 5)
= 2\(x^2\) - 4\(x\) - 21
b, (3\(x^2\) - 2\(xy\) + 4) + (5\(xy\) - 6\(x^2\) - 7)
= 3\(x^2\) - 2\(xy\) + 4 + 5\(xy\) - 6\(x^2\) - 7
= (3\(x^2\) - 6\(x^2\)) + (5\(xy\) - 2\(xy\)) - (7 - 4)
= - 3\(x^2\) + 3\(xy\) - 3
Bài 2:
a, 3\(x^2\).(2\(x\) + y) - 2y(4\(x^2\) - y)
= 6\(x^3\) + 3\(x^2\).y - 8y\(x^2\) + 2y2
= 6\(x^3\) - (8\(x^2\)y - 3\(x^2\)y) + 2y2
= 6\(x^3\) - 5\(x^2\)y + 2y2