How do you combine like terms in #3( 2a - b ) - 7( 3b - 5a )#?

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Answer 1 · 2018-05-13T04:38:00

#41a - 5b#

Before we combine like terms, we first use the distributive property, as shown here:
cdn.virtualnerd.com

Following this image, we can distribute/expand #color(blue)(3(2a-b))# and #color(blue)(-7(3b-5a))#.

#color(blue)(3(2a-b) = 6a - 3b)#

#color(blue)(-7(3b-5a) = -21b + 35a)#

Now put these back into the expression:
#6a - 3b - 21b + 35a#

Now let's color-code the like terms:
#color(red)(6a) quadcolor(green)(-quad3b) quadcolor(green)(-quad2b) quadcolor(red)(+quad35a)#

Combine like terms:
#41a - 5b#

Hope this helps!