# Simplify (2ax+ay)/(ax-4a)*(4bx+2by)/(2bx-8b)

2ax+ayax-4a⋅4bx+2by2bx-8b
Factor a out of 2ax+ay.
Factor a out of 2ax.
a(2x)+ayax-4a⋅4bx+2by2bx-8b
Factor a out of ay.
a(2x)+a(y)ax-4a⋅4bx+2by2bx-8b
Factor a out of a(2x)+a(y).
a(2x+y)ax-4a⋅4bx+2by2bx-8b
a(2x+y)ax-4a⋅4bx+2by2bx-8b
Factor a out of ax-4a.
Factor a out of ax.
a(2x+y)a(x)-4a⋅4bx+2by2bx-8b
Factor a out of -4a.
a(2x+y)a(x)+a⋅-4⋅4bx+2by2bx-8b
Factor a out of a(x)+a⋅-4.
a(2x+y)a(x-4)⋅4bx+2by2bx-8b
a(2x+y)a(x-4)⋅4bx+2by2bx-8b
Factor 2b out of 4bx+2by.
Factor 2b out of 4bx.
a(2x+y)a(x-4)⋅2b(2x)+2by2bx-8b
Factor 2b out of 2by.
a(2x+y)a(x-4)⋅2b(2x)+2b(y)2bx-8b
Factor 2b out of 2b(2x)+2b(y).
a(2x+y)a(x-4)⋅2b(2x+y)2bx-8b
a(2x+y)a(x-4)⋅2b(2x+y)2bx-8b
Factor 2b out of 2bx-8b.
Factor 2b out of 2bx.
a(2x+y)a(x-4)⋅2b(2x+y)2b(x)-8b
Factor 2b out of -8b.
a(2x+y)a(x-4)⋅2b(2x+y)2b(x)+2b(-4)
Factor 2b out of 2b(x)+2b(-4).
a(2x+y)a(x-4)⋅2b(2x+y)2b(x-4)
a(2x+y)a(x-4)⋅2b(2x+y)2b(x-4)
Cancel the common factor of a.
Cancel the common factor.
a(2x+y)a(x-4)⋅2b(2x+y)2b(x-4)
Rewrite the expression.
2x+yx-4⋅2b(2x+y)2b(x-4)
2x+yx-4⋅2b(2x+y)2b(x-4)
Cancel the common factor of 2.
Cancel the common factor.
2x+yx-4⋅2b(2x+y)2b(x-4)
Rewrite the expression.
2x+yx-4⋅b(2x+y)b(x-4)
2x+yx-4⋅b(2x+y)b(x-4)
Cancel the common factor of b.
Cancel the common factor.
2x+yx-4⋅b(2x+y)b(x-4)
Rewrite the expression.
2x+yx-4⋅2x+yx-4
2x+yx-4⋅2x+yx-4
Multiply 2x+yx-4⋅2x+yx-4.
Multiply 2x+yx-4 and 2x+yx-4.
(2x+y)(2x+y)(x-4)(x-4)
Raise 2x+y to the power of 1.
(2x+y)1(2x+y)(x-4)(x-4)
Raise 2x+y to the power of 1.
(2x+y)1(2x+y)1(x-4)(x-4)
Use the power rule aman=am+n to combine exponents.
(2x+y)1+1(x-4)(x-4)
(2x+y)2(x-4)(x-4)
Raise x-4 to the power of 1.
(2x+y)2(x-4)1(x-4)
Raise x-4 to the power of 1.
(2x+y)2(x-4)1(x-4)1
Use the power rule aman=am+n to combine exponents.
(2x+y)2(x-4)1+1