(m%2B1)-(3m%2B5)(9-5m).jpeg "(m+2)(m+1)-(3m+5)(9-5m)")
Simplifying the Expression: (m+2)(m+1)-(3m+5)(9-5m)
This article will guide you through simplifying the expression (m+2)(m+1)-(3m+5)(9-5m).
Step 1: Expanding the Products
We begin by expanding the products using the distributive property (also known as FOIL method):
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(m+2)(m+1) = m(m+1) + 2(m+1) = m² + m + 2m + 2 = m² + 3m + 2
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(3m+5)(9-5m) = 3m(9-5m) + 5(9-5m) = 27m - 15m² + 45 - 25m = -15m² + 2m + 45
Step 2: Combining Like Terms
Now we substitute the expanded products back into the original expression:
(m+2)(m+1)-(3m+5)(9-5m) = (m² + 3m + 2) - (-15m² + 2m + 45)
Next, we remove the parentheses by distributing the negative sign:
= m² + 3m + 2 + 15m² - 2m - 45
Finally, we combine the like terms:
= 16m² + m - 43
Conclusion
Therefore, the simplified form of the expression (m+2)(m+1)-(3m+5)(9-5m) is 16m² + m - 43.