(2a-3)(a+7)+2a(5-a)

less than a minute read Jun 16, 2024
(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.

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