How do you use the distributive property to simplify #(4)(2x - 5) - 2(3x^2 - 2)#?

#4(2x-5) - 2(3x^2-2)#

To simplify this, we use the distributive property (shown below):
#http://cdn.virtualnerd.com/thumbnails/Alg1_1l-diagram_thumb-lgpng#

Following this image, we know that:
#color(blue)(4(2x-5) = (4 * 2x) + (4 * -5) = 8x - 20)#
and
#color(blue)(-2(3x^2-2) = (-2 * 3x^2) + (-2 * -2) = -6x^2 + 4)#

Combine them:
#8x-20 - 6x^2 + 4#

Combine the like terms #color(blue)(-20)# and #color(blue)(4)#:
#8x - 16 - 6x^2#

Since we typically write it when the highest exponent degree first, it becomes:
#-6x^2 + 8x -16#

Hope this helps!

The distributive law is applied to multiply a monomial factor into a bracket.

The number outside is multiplied by each term inside the bracket:

#color(red)(a)(color(blue)(b+c+d)) = color(red)(a)color(blue)(b)+color(red)(a)color(blue)(c)+color(red)(a)color(blue)(d)#

#" "color(red)((4))(color(blue)(2x-5))- color(green)((2))(color(purple)(3x^2-2))#

#= color(red)(4)color(blue)((2x))+color(red)(4)color(blue)((-5))-color(green)(2)color(purple)((3x^2))-color(green)(2)color(purple)((-2))#
#color(white)(xxxx)darrcolor(white)(xxxx)darrcolor(white)(xxxx)darrcolor(white)(xxxx)darr#
#=" "8x" "-20" " -6x^2" "+4" "larr# collect like terms

#=-6x^2+8x-16#