Answer:
27. 3(9 + 4)
28. 6(2 + 6)
29. 4(4 + 5)
30. 2(x + 4)
31. 6(5 + 2x
32. 7(6x + 7)
Step-by-step explanation:
These six problems are basically the same, so I will just explain the first one.
27. 27 + 12 =
To factor expressions, find their greatest common factors.
If you can't come up with the GCF off the top of your head, all you have to do is list out each number's factors.
27's factors: 1, 3, 9, 27
12's factors: 1, 2, 3, 4, 6, 12
If you look at these two lists, you can see that 3 is the largest number that they both share.
To factor them, divide both numbers by the GCF, which is 3.
27/3 = 9
12/3 = 4
This is basically pulling a number out of the original addition expression.
You start with 27 + 12.
You can pull out a 3, as we found out just now.
Now you have (3 x 9) + (3 x 4)
You can take out the 3 to get 3(9 + 4) because of the distributive property.
And that's all!
28. 12 + 36 =
(6 x 2) + (6 x 6)
6(2 + 6)
29. 16 + 20 =
(4 x 4) + (4 x 5)
4(4 + 5)
30. 2x + 8 =
(Same rules apply to terms with variables!)
(2 x x) + (2 x 4)
2(x + 4)
31. 30 + 12x
(6 x 5) + (6 x 2x)
6(5 + 2x)
32. 42x + 49
(7 x 6x) + (7 x 7)
7(6x + 7)
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