%E2%8B%85(%E2%88%925).jpeg "(−2a+5−b)⋅(−5)")
Simplifying the Expression: (-2a + 5 - b) ⋅ (-5)
This article will guide you through the process of simplifying the algebraic expression (-2a + 5 - b) ⋅ (-5).
Understanding the Problem
The expression involves multiplication of a trinomial (-2a + 5 - b) by a constant (-5). Our goal is to distribute the constant across each term within the trinomial and simplify the result.
Applying the Distributive Property
The distributive property states that for any numbers a, b, and c: a ⋅ (b + c) = a ⋅ b + a ⋅ c
We can apply this to our expression:
(-2a + 5 - b) ⋅ (-5) = (-5) ⋅ (-2a) + (-5) ⋅ 5 + (-5) ⋅ (-b)
Simplifying the Terms
Now, let's multiply each term:
- (-5) ⋅ (-2a) = 10a
- (-5) ⋅ 5 = -25
- (-5) ⋅ (-b) = 5b
The Simplified Expression
Combining the simplified terms, we get the final simplified expression:
(-2a + 5 - b) ⋅ (-5) = 10a - 25 + 5b
Conclusion
By applying the distributive property and simplifying each term, we have successfully simplified the expression (-2a + 5 - b) ⋅ (-5) to 10a - 25 + 5b. This expression is now in its simplest form.