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

Question

1930 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-05-13T04:38:00

$41 a - 5 b$ $41a - 5b$

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

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

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

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

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

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!

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