#16x^3y^4+8x^2y^3#
Let us write the factors of the terms given to us:
#16x^3y^4=2xx2xx2xx2xx x xx x xx x xx yxxyxxyxxy#
#8x^2y^3=2xx2xx2xx x xx x xxyxxyxxy#
Now, let us mark the common factors between the two terms:
#16x^3y^4=color(red)(2)xxcolor(red)(2)xxcolor(red)(2)xx2xx color(red)(x) xx color(red)(x) xx x xx color(red)(y)xxcolor(red)(y)xxcolor(red)(y)xxy#
#8x^2y^3=color(red)(2)xxcolor(red)(2)xxcolor(red)(2)xx color(red)(x) xx color(red)(x) xxcolor(red)(y)xxcolor(red)(y)xxcolor(red)(y)#
Write the common factors and put the remaining factors in brackets, with the appropriate sign:
#=color(red)(2)xxcolor(red)(2)xxcolor(red)(2)xx color(red)(x) xx color(red)(x) xxcolor(red)(y)xxcolor(red)(y)xxcolor(red)(y) ( color(blue)(2)xxcolor(blue)(x)xxcolor(blue)(y) + color(green)(1))#
#=color(red)(8x^2y^3)(color(blue)(2xy)+color(green)(1))#
Therefore, the factor of #16x^3y^4+8x^2y^3 = 8x^2y^3(2xy+1)#
