(x+3)(x+7) Solve Using Identity

Jasonbradley

2 min read

·

Jun 16, 2024

31

Share

Solving (x+3)(x+7) using the Identity

The expression (x+3)(x+7) can be solved using the distributive property or by using the identity (a+b)(a+c) = a² + a(b+c) + bc. Let's explore both methods.

Using the Distributive Property

1. Distribute the first term: (x+3)(x+7) = x(x+7) + 3(x+7)

2. Distribute further: x(x+7) + 3(x+7) = x² + 7x + 3x + 21

3. Combine like terms: x² + 7x + 3x + 21 = x² + 10x + 21

Using the Identity

1. Identify 'a', 'b', and 'c': In this case, a = x, b = 3, and c = 7.

2. Apply the identity: (a+b)(a+c) = a² + a(b+c) + bc (x+3)(x+7) = x² + x(3+7) + 3 * 7

3. Simplify: x² + x(3+7) + 3 * 7 = x² + 10x + 21

Conclusion

As you can see, both methods lead to the same answer: x² + 10x + 21. Using the identity provides a more concise solution and can be useful for simplifying more complex expressions. It's important to understand both methods and choose the one that suits the specific problem best.