Pregunta
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\( (2a + 3)^2 = 4a^2 + 12a + 9 \)
Solución
To expand the expression \( (2a + 3)^2 \), you can use the formula for squaring a binomial:
\[
(A + B)^2 = A^2 + 2AB + B^2
\]
Here, \( A = 2a \) and \( B = 3 \). Applying the formula:
\[
(2a + 3)^2 = (2a)^2 + 2 \cdot (2a) \cdot 3 + 3^2
\]
Calculate each term:
1. \( (2a)^2 = 4a^2 \)
2. \( 2 \cdot (2a) \cdot 3 = 12a \)
3. \( 3^2 = 9 \)
Combine all the terms:
\[
(2a + 3)^2 = 4a^2 + 12a + 9
\]
**Final Answer:**
\[
(2a + 3)^2 = 4a^2 + 12a + 9
\]
Respondido por UpStudy AI y revisado por un tutor profesional
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Simplifique esta solución The Deep Dive
Did you know that squaring a binomial like \( (2a + 3) \) is governed by the formula \( (x + y)^2 = x^2 + 2xy + y^2 \)? So, applying that here, you get \( (2a)^2 + 2 \times (2a) \times 3 + 3^2 \), which expands to \( 4a^2 + 12a + 9 \)! Now, in the real world, concepts like this are everywhere, from calculating areas to predicting project costs! For example, if you're designing a garden bed that's shaped like a square made by \( (2a + 3) \), you'll need this expansion to find out how much soil to buy, taking both the area and depth into account. How cool is that?
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