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:
\(a,\left(3x+1\right)^2-\left(3x-1\right)^2\\
=\left(3x+1-3x+1\right)\left(3x+1+3x-1\right)\\
=2\cdot6x\\
=12x\\
b,\left(x+y\right)^2-\left(x-y\right)^2\\
=\left(x+y-x+y\right)\left(x+y+x-y\right)\\
=2y\cdot2x\\
=4xy\\
c,\left(x+y\right)^3-\left(x-y\right)^3\\
=\left(x+y-x+y\right)\left[\left(x+y\right)^2+\left(x+y\right)\left(x-y\right)+\left(x-y\right)^2\right]\\
=2y\left(x^2+2xy+y^2+x^2-y^2+x^2-2xy+y^2\right)\\
=2y\left(3x^2+y^2\right)\)