ANSWER
12r + t - 4r + 6t => 8r + 7t
(12r + 2t) - (4r + 10t) => 8(r - t)
12(r + t) - 6(r + t) + 4(r + t) - 2(r + t) => 8(r + t)
Step-by-step explanation
We want to find the expressions in A that are equivalent to the expressions in B.
To do this, we have to simplify each expression in Column A and then find the equivalent expression in Column B.
FIRST ONE:
12r + t - 4r + 6t
To simplify, collect like terms:
12r - 4r + t + 6t
=> 8r + 7t
SECOND ONE:
(12r + 2t) - (4r + 10t)
First, expand the brackets, then collect like terms:
12r + 2t - 4r - 10t
=> 12r - 4r + 2t - 10t
8r - 8t
This can be further factorized:
8(r - t)
THIRD ONE:
12(r + t) - 6(r + t) + 4(r + t) - 2(r + t)
Expand the brackets and collect like terms:
12r + 12t - 6r - 6t + 4r + 4t - 2r - 2t
=> 12r - 6r + 4r - 2r + 12t - 6t + 4t - 2t
8r + 8t
This can be further factorized:
8(r + t)
Those are the equivalent expressions from Columns A and B.