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a) 85 .12,7 + 5.3.12,7 = 12,7 . ( 85 + 5.3 ) = 12,7 . (85+15) = 12,7 . 100 = 1270
b) 52.143 - 52.39 - 8.26 = 52.143 - 52.39 - 4.2.26 = 52.143 - 52.39 - 4.52 = 52.( 143 -39 - 4 ) = 52 . 100 = 5200
phân tích :
5x - 20y = 5 .(x - 4y)
5x(x-1)-3x.(x-1) = (x-1).(5x-3x) = 2x(x-1) hoặc 5x(x-1)-3x(x-1) = x(x-1)(5-3) = 2x(x-1)
x.(x+y)-5x-5y = x(x+y) - 5 (x+y) = (x+y)(x-5)
a.
\(x^2+xy+x=x\left(x+y+1\right)\)
Tại \(x=77;y=22\Rightarrow x\left(x+y+1\right)=77\left(77+22+1\right)=77.100=7700\)
b.
\(x\left(x-y\right)+y\left(y-x\right)=x\left(x-y\right)-y\left(x-y\right)=\left(x-y\right)\left(x-y\right)=\left(x-y\right)^2\)
\(=\left(53-3\right)^2=50^2=2500\)
c.
\(x\left(x-1\right)-y\left(1-x\right)=x\left(x-1\right)+y\left(x-1\right)=\left(x+y\right)\left(x-1\right)\)
\(=\left(2001+1999\right)\left(2001-1\right)=4000.2000=8000000\)
tính nhanh
85.12,7+5.3.12,7
52.143-52.39-8.26
phân tích thành nhân tử
5X-20Y
5x(x-1)-3x(x-1)
x(x+y)-5x-5y
tính nhanh .
a) 85 .12,7 + 5.3.12,7 = 12,7 . ( 85 + 5.3 ) = 12,7 . (85+15) = 12,7 . 100 = 1270
b) 52.143 - 52.39 - 8.26 = 52.143 - 52.39 - 4.2.26 = 52.143 - 52.39 - 4.52 = 52.( 143 -39 - 4 ) = 52 . 100 = 5200
phân tích :
5x - 20y = 5 .(x - 4y)
5x(x-1)-3x.(x-1) = (x-1).(5x-3x) = 2x(x-1) hoặc 5x(x-1)-3x(x-1) = x(x-1)(5-3) = 2x(x-1)
x.(x+y)-5x-5y = x(x+y) - 5 (x+y) = (x+y)(x-5)
a)-(x-y)(x2+xy-1)=-(x3+x2y-x-x2y-xy2+y)
=-(x3-xy2-x+y)
=-x3+xy2+x-y
b)x2(x-1)-(x3+1)(x-y)=x3-x2-x3+x2y-x+y
=-x2+x2y-x+y
c)(3x-2)(2x-1)+(-5x-1)(3x+2)=6x2-3x-4x+2-15x2-10x-3x-2
=-9x2-20x
d) hình như bạn ghi lỗi
Bài 2: C=x(x2-y)-x2(x+y)+y(x2-x)
=x3-xy-x3-x2y+x2y-xy
=-2xy
Thay x=1/2,y=-1 vào C, ta có:
C=-2.1/2.(-1)=1
Vậy C=1 khi x=1/2 và y=-1.
Bài 2:
a: \(x^2+5x-6=\left(x+6\right)\left(x-1\right)\)
b: \(5x^2+5xy-x-y\)
\(=5x\left(x+y\right)-\left(x+y\right)\)
\(=\left(x+y\right)\left(5x-1\right)\)
c:\(-6x^2+7x-2\)
\(=-6x^2+3x+4x-2\)
\(=-3x\left(2x-1\right)+2\left(2x-1\right)\)
\(=\left(2x-1\right)\left(-3x+2\right)\)
1.
a) \(=x^2\left(x^2+2x+1\right)=x^2\left(x+1\right)^2\)
b) \(=\left(x+y\right)^3-\left(x+y\right)=\left(x+y\right)\left[\left(x+y\right)^2-1\right]\)
\(=\left(x+y\right)\left(x+y-1\right)\left(x+y+1\right)\)
c) \(=5\left[\left(x^2-2xy+y^2\right)-4z^2\right]=5\left[\left(x-y\right)^2-4z^2\right]\)
\(=5\left(x-y-2z\right)\left(x-y+2z\right)\)
2.
a) \(=x\left(x+2\right)+3\left(x+2\right)=\left(x+2\right)\left(x+3\right)\)
b) \(=5x\left(x+y\right)-\left(x+y\right)=\left(x+y\right)\left(5x-1\right)\)
c) \(=-\left[3x\left(2x-1\right)-2\left(2x-1\right)\right]=-\left(2x-1\right)\left(3x-2\right)\)
3.
b) \(=2x\left(x-1\right)+5\left(x-1\right)=\left(x-1\right)\left(2x+5\right)\)
c) \(=-\left[5x\left(x-3\right)-1\left(x-3\right)\right]=-\left(x-3\right)\left(5x-1\right)\)
4.
a) \(\Rightarrow\left(x-1\right)\left(5x-1\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=1\\x=\dfrac{1}{5}\end{matrix}\right.\)
b) \(\Rightarrow2\left(x+5\right)-x\left(x+5\right)=0\)
\(\Rightarrow\left(x+5\right)\left(2-x\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=-5\\x=2\end{matrix}\right.\)
Bài 2:
a: Ta có: \(2\left(5x-8\right)-3\left(4x-5\right)=4\left(3x-4\right)+11\)
\(\Leftrightarrow10x-16-12x+15=12x-16+11\)
\(\Leftrightarrow-14x=-4\)
hay \(x=\dfrac{2}{7}\)
b: Ta có: \(2x\left(6x-2x^2\right)+3x^2\left(x-4\right)=8\)
\(\Leftrightarrow12x^2-4x^3+3x^3-12x^2=8\)
\(\Leftrightarrow x^3=-8\)
hay x=-2
Bài 1:
a: Ta có: \(I=x\left(y^2-xy^2\right)+y\left(x^2y-xy+x\right)\)
\(=xy^2-x^2y^2+x^2y^2-xy^2+xy\)
\(=xy\)
=1
b: Ta có: \(K=x^2\left(y^2+xy^2+1\right)-\left(x^3+x^2+1\right)\cdot y^2\)
\(=x^2y^2+x^3y^2+x^2-x^3y^2-x^2y^2-y^2\)
\(=x^2-y^2\)
\(=\dfrac{1}{4}-\dfrac{1}{4}=0\)
a) Kết quả M = 0. Chú ý: nhân tử chung là 2f - 5 = 0.
b) Kết quả N = 300000.
c) Kết quả p = 0. Chú ý: nhân tử x 2 + y -1 = 0.
d) Kết quả Q = 280. Chú ý: Q = (x - y)[ ( x - y ) 2 - xy].
1/
a)5x – 20y=5(x-4y)
b) 5x.(x – 1) – 3x(x – 1)=2x(x-1)
c) x.(x+y) – 5x – 5y=c) x.(x+y) – 5(x+y)=(x-5)(x+y)
2/
a)x2 + xy + x = x(x+y+1)=77.(77+22+1)=77.100=7700
b) x . ( x – y ) + y . ( y – x )=(x-y)(x-y)=(x-y)2=(53-3)2=2500
3/
a) X + 5x2 = 0
⇒x(x+5)=0
⇒hoặc x=0
x+5=0⇒x=-5
b)x + 1 = ( x + 1 )2
⇒(x + 1)-( x + 1 )2 =0
⇒x(x+1)=0
⇒ hoặc x=0
hoặc x+1=0⇒x=-1
4/
a) 97 . 13 + 130 . 0,3 = 97.13+13.10.0,3=97.13+13.3=100.13=1300
b)86 . 153 – 530 . 8,6=86.153–53.10.8,6=86.153-53.86=86.100=8600
C) 85 .12,7 + 5,3 . 12,7= 12,7(85+5,3)=12,7.90,3=1146,81
D)52.143 – 52 . 39 – 8.26=52(143-39)-8,26=52.104-8,26=5399,74