Bài 1 Phân tích các đa thức sau
a,4x^2-6x
b,x^3y-2x^2y+5xy
c,2x^2(x+1) +4x(x+1)
d,2/5x×(y-1) -2/5y×(1-y)
Bài 2 tính bằng cách hợp lý
a, 8,4×84, 5+840×0, 155
b, 0,78×1300+50×6, 5-39
c,0, 12×90-110×0, 6+36-25×6
Bài 3 Phân tích các đa thức sau
a, (3x+1) ^2-(3x-1) ^2
b, (x+y) ^2-(x-y) ^2
c,(x+y)^3-(x-y) ^3
Bài 1:Phân tích các đa thức sau:
\(a,4x^2-6x\\ =2x(2x-3)\\ b,x^3y-2x^2y+5xy\\ = xy(x^2-2x+5)\\ c,2x^2(x+1) +4x(x+1)\\ =2x(x+1)(x+2)\\ d,\frac{2}{5}x.(y-1) -\frac{2}{5}x.(1-y)\\ =\frac{2}{5}x.(y-1)+\frac{2}{5}x.(y-1)\\ =2.\bigg[\frac{2}{5}x.(y-1)\bigg]\)
Bài 2 tính bằng cách hợp lý
\(a, 8,4.84, 5+840.0, 155\\ =8,4.(84,5+100.0,155)\\ =8,4.100\\ =840\\ b, 0,78.1300+50.6, 5-39\\ =(0,78.1300-39)+50. 6,5\\ =0,78.(1300-50)+50. 6,5\\ =0,78.1250+50. 6,5\\ =50.(0,78.25+6,5)\\ =1300\\ c,0, 12.90-110.0, 6+36-25.6\\ =6.(15.0,12-110.0,1+6-25)\\ =6.-28,2\\ =-169.2\)
Bài 3 Phân tích các đa thức sau\(a, (3x+1) ^2-(3x-1) ^2\\ =(3x+1-3x+1)(3x+1+3x-1)\\ =2.6x\\ b, (x+y) ^2-(x-y) ^2\\ =(x+y-x+y)(x+y+x-y)\\ =2y.2x\\ =2.(x-y)\\ c,(x+y)^3-(x-y) ^3\\ =(x+y-x+y)\bigg[(x+y)^2+(x+y)(x-y)+(x-y)^2\bigg]\\ =2y(x^2+2xy+y^2+x^2-xy+xy-y^2+x^2-2xy+y^2)\\ =2y(3x^2+y^2)\)
Bài 1:
\(a,4x^2-6x=2x\left(2x-3\right)\\ b,x^3y-2x^2y+5xy=xy\left(x^2-2x+5\right)\\ c,2x^2\left(x+1\right)+4x\left(x+1\right)=2x\left(x+1\right)\left(x+2\right)\\ d,\frac{2}{5}x\left(y-1\right)-\frac{2}{5}y\left(1-y\right)\\ =\frac{2}{5}\left(y-1\right)\left(x+y\right)\)
Bài 2:
\(a,8,4\cdot84,5+840\cdot0,155\\ =840\left(0,845+0,155\right)\\ =840\cdot1=840\\ b,0,78\cdot1300+50\cdot6,5-39\\ =39\cdot2\cdot13-39+25\cdot2\cdot6,5\\ =39\left(26-1\right)+25\cdot13\\ =39\cdot25+25\cdot13\\ =25\left(39+13\right)\\ =25\cdot52\\ =1300\\ c,0,12\cdot90-110\cdot0,6+36-25\cdot6\\ =6\cdot2\cdot0,9-6\cdot11+6\cdot6-25\cdot6\\ =6\left(1,8-11+6-25\right)\\ =-28,2\cdot6\\ =-169,2\)
Bài 3:
\(a,\left(3x+1\right)^2-\left(3x-1\right)^2\\ =\left(3x+1-3x+1\right)\left(3x+1+3x-1\right)\\ =2\cdot6x\\ =12x\\ b,\left(x+y\right)^2-\left(x-y\right)^2\\ =\left(x+y-x+y\right)\left(x+y+x-y\right)\\ =2y\cdot2x\\ =4xy\\ c,\left(x+y\right)^3-\left(x-y\right)^3\\ =\left(x+y-x+y\right)\left[\left(x+y\right)^2+\left(x+y\right)\left(x-y\right)+\left(x-y\right)^2\right]\\ =2y\left(x^2+2xy+y^2+x^2-y^2+x^2-2xy+y^2\right)\\ =2y\left(3x^2+y^2\right)\)