(4t+3)^2

Jasonbradley

2 min read

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Jun 16, 2024

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Expanding (4t + 3)²

In algebra, expanding an expression means rewriting it without any parentheses. This is often done using the distributive property or by recognizing a pattern. Let's explore how to expand (4t + 3)².

Using the Distributive Property

The distributive property states that a(b + c) = ab + ac. We can apply this property to expand (4t + 3)²:

1. Rewrite (4t + 3)² as (4t + 3)(4t + 3).
2. Apply the distributive property:
   • (4t + 3)(4t + 3) = 4t(4t + 3) + 3(4t + 3)
3. Distribute again:
   • 4t(4t + 3) + 3(4t + 3) = 16t² + 12t + 12t + 9
4. Combine like terms:
   • 16t² + 12t + 12t + 9 = 16t² + 24t + 9

Using the Pattern (a + b)²

Another way to expand (4t + 3)² is to recognize the pattern (a + b)² = a² + 2ab + b²

1. Identify a and b: In this case, a = 4t and b = 3.
2. Substitute into the pattern:
   • (4t)² + 2(4t)(3) + (3)²
3. Simplify:
   • 16t² + 24t + 9

The Result

Both methods lead us to the same expanded form of (4t + 3)²: 16t² + 24t + 9.