Pregunta
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\((p + q)^2 = p^2 + 2pq + q^2\)
Solución
To expand the expression \((p + q)^2\), you can use the **binomial expansion formula**:
\[
(a + b)^2 = a^2 + 2ab + b^2
\]
Applying this to \((p + q)^2\):
\[
(p + q)^2 = p^2 + 2pq + q^2
\]
**Breakdown:**
1. **First Term (\(p^2\))**: Square the first term \(p\).
2. **Middle Term (\(2pq\))**: Multiply both terms together and then double the product.
3. **Last Term (\(q^2\))**: Square the second term \(q\).
**Final Expanded Form:**
\[
(p + q)^2 = p^2 + 2pq + q^2
\]
Revisado y aprobado por el equipo de tutoría de UpStudy
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Simplifique esta solución Mind Expander
Did you know that the expression \( (p+q)^{2} \) can be expanded using the classic binomial theorem? This cute little formula says that you can break it down into \( p^2 + 2pq + q^2 \). It's not just a math trick; it actually helps us understand polynomial identities better! In real life, this expansion can be handy in various fields like physics or economics when dealing with squared terms. For example, if you’re calculating areas (like in garden design!) or predicting profits, this algebraic expression can simplify your work and make calculations much smoother. Isn't math awesome?
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