(a-b+3c) ×(a+2b)
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To simplify the expression (a-b+3c) × (a+2b), we can use the distributive property. This property states that multiplying a sum by a number is the same as multiplying each term in the sum by that number and then adding the results.
Using this property, we can expand the expression as follows:
(a-b+3c) × (a+2b) = a(a+2b) - b(a+2b) + 3c(a+2b)
Now, let's simplify each term:
1. Multiplying a by (a+2b):
a(a+2b) = a^2 + 2ab
2. Multiplying -b by (a+2b):
-b(a+2b) = -ba - 2b^2
3. Multiplying 3c by (a+2b):
3c(a+2b) = 3ca + 6cb
Now, let's combine the simplified terms:
(a-b+3c) × (a+2b) = a^2 + 2ab - ba - 2b^2 + 3ca + 6cb
To further simplify, we can combine like terms:
a^2 - ba + 3ca + 2ab + 6cb - 2b^2
And that is the simplified form of the expression (a-b+3c) × (a+2b).