a/ \(2\left(x+y\right)-5a\left(x+y\right)\)
\(=\left(x+y\right)\left(2-5a\right)\)
b/\(a^2\left(x-5\right)-3\left(x-5\right)\)
\(=\left(x-5\right)\left(a^2-3\right)\)
c/ \(4x\left(a-b\right)+6xy\left(a-b\right)\)
\(=\left(a-b\right)\left(4x+6xy\right)\)
\(=\left(a-b\right).2x\left(2+3y\right)\)
d/ \(y\left(a-b\right)-x\left(b-a\right)\)
\(=y\left(a-b\right)+x\left(a-b\right)\)
\(=\left(a-b\right)\left(y+x\right)\)
e/ \(6x\left(x-y\right)+8y\left(y-x\right)\)
\(=6x\left(x-y\right)-8y\left(x-y\right)\)
\(=\left(x-y\right)\left(6x-8y\right)\)
\(=\left(x-y\right).2\left(3x-4y\right)\)
f/ \(4\left(x-3\right)^2-2x\left(x-3\right)\)
\(=\left(x-3\right)\left(4\left(x-3\right)-2x\right)\)
\(=\left(x-3\right)\left(2x-12\right)\)
\(=\left(x-3\right).2\left(x-6\right)\)
a) \(2\left(x+y\right)-5a\left(x+y\right)=\left(x+y\right)\left(2-5a\right)\)
b) \(a^2\left(x-5\right)-3\left(x-5\right)=\left(x-5\right)\left(a^2-3\right)\)
c) \(4x\left(a-b\right)+6xy\left(a-b\right)=2x\left(a-b\right)\left(2+3y\right)\)
d) \(y\left(a-b\right)-x\left(b-a\right)=y\left(a-b\right)+x\left(a-b\right)=\left(a-b\right)\left(x+y\right)\)