Think of 2 apples + 3 bananas + 4 apples.
What can be added together?
6 apples + 3 bananas
6a+3b
11a+7b-(3b-2a)
2 x (2a + 3b - 6)
3a + (3b - 2a) + 5b =3a + 3b - 2a + 5b =(3a - 2a) + (3b + 5b) =a + 8b
1a+3b 2a+4b=3a +7b
(6ab + 9b)/(2a + 3) = 3b(2a + 3)/(2a + 3) = 3b
8b -2a
11a+7b-(3b-2a)
2a+(-11b)
To simplify the expression (2(2a + 3b)), you distribute the 2 to both terms inside the parentheses. This results in (2 \cdot 2a + 2 \cdot 3b), which simplifies to (4a + 6b). Thus, the final result is (4a + 6b).
2 x (2a + 3b - 6)
3a + (3b - 2a) + 5b =3a + 3b - 2a + 5b =(3a - 2a) + (3b + 5b) =a + 8b
2A plus 3B times 2A - 3B = 4A2 - 9B2; this is an example of the general formula (a + b)(a - b) = a2 - b2.
(2a + b)(a + 3b)
6 is the average of 2a and a - 2b so 12 = 2a + a - 2b = 3a - 2b3 is the average of 2a - b and 4a + 3b so 6 = 2a - b + 4a + 3b = 6a + 2bAdding the two equations gives: 18 = 9a so that a = 2Substituting for a in the first gives 12 = 6 - 2b so that b = -36 is the average of 2a and a - 2b so 12 = 2a + a - 2b = 3a - 2b3 is the average of 2a - b and 4a + 3b so 6 = 2a - b + 4a + 3b = 6a + 2bAdding the two equations gives: 18 = 9a so that a = 2Substituting for a in the first gives 12 = 6 - 2b so that b = -36 is the average of 2a and a - 2b so 12 = 2a + a - 2b = 3a - 2b3 is the average of 2a - b and 4a + 3b so 6 = 2a - b + 4a + 3b = 6a + 2bAdding the two equations gives: 18 = 9a so that a = 2Substituting for a in the first gives 12 = 6 - 2b so that b = -36 is the average of 2a and a - 2b so 12 = 2a + a - 2b = 3a - 2b3 is the average of 2a - b and 4a + 3b so 6 = 2a - b + 4a + 3b = 6a + 2bAdding the two equations gives: 18 = 9a so that a = 2Substituting for a in the first gives 12 = 6 - 2b so that b = -3
4a
1a+3b 2a+4b=3a +7b
(6ab + 9b)/(2a + 3) = 3b(2a + 3)/(2a + 3) = 3b