Which of the following expressions have the same value?
(6b+3)(−2+a)
(2b+1)(3a−6)
(a+3)(6b−2)
6ab+3a−12b−6
To solve this problem, we need to systematically expand and simplify each expression given in the problem statement:
Expression 1: (6b+3)(−2+a)
Expand using the distributive property:
=6b(−2)+6b(a)+3(−2)+3(a)
=−12b+6ab−6+3a
Reorder terms: 6ab+3a−12b−6
Expression 2: (2b+1)(3a−6)
Expand using the distributive property:
=2b(3a)+2b(−6)+1(3a)+1(−6)
=6ab−12b+3a−6
This simplifies directly to 6ab+3a−12b−6
Expression 3: (a+3)(6b−2)
Expand using the distributive property:
=a(6b)+a(−2)+3(6b)+3(−2)
=6ab−2a+18b−6
This results in 6ab−2a+18b−6, clearly different from the others
Expression 4: 6ab+3a−12b−6
This is already simplified and the same as the results of expressions 1 and 2.
Upon comparing the simplified expressions, expressions 1, 2, and 4 have the same value: 6ab+3a−12b−6. Expression 3 differs with 6ab−2a+18b−6.
Thus, the expressions with the same value are 1, 2, and 4.
Therefore, the correct answer is choice 4: 1,2,4.