(a%2B7)%2B2a(5-a).jpeg "(2a-3)(a+7)+2a(5-a)")
Simplifying the Expression (2a-3)(a+7)+2a(5-a)
This article will guide you through simplifying the expression (2a-3)(a+7)+2a(5-a).
Step 1: Expand the Products
We begin by expanding the products using the distributive property:
- (2a-3)(a+7) = 2a(a+7) - 3(a+7) = 2a² + 14a - 3a - 21 = 2a² + 11a - 21
- 2a(5-a) = 10a - 2a²
Step 2: Combine Like Terms
Now, we combine the expanded terms:
(2a² + 11a - 21) + (10a - 2a²)
2a² + 11a - 21 + 10a - 2a²
Step 3: Simplify
The terms 2a² and -2a² cancel each other out, leaving us with:
11a - 21 + 10a
Combining like terms:
21a - 21
Conclusion
Therefore, the simplified form of the expression (2a-3)(a+7)+2a(5-a) is 21a - 21.