Question
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Answer
\( (2x - 3)(2x + 5) = 4x^2 + 4x - 15 \)
Solution
Para multiplicar los binomios \( (2x - 3)(2x + 5) \), seguimos los siguientes pasos:
1. **Aplicar la propiedad distributiva (FOIL)**:
\[
(2x - 3)(2x + 5) = 2x \cdot 2x + 2x \cdot 5 - 3 \cdot 2x - 3 \cdot 5
\]
2. **Realizar las multiplicaciones**:
\[
= 4x^2 + 10x - 6x - 15
\]
3. **Simplificar los términos semejantes**:
\[
= 4x^2 + (10x - 6x) - 15
\]
\[
= 4x^2 + 4x - 15
\]
**Resultado final:**
\[
(2x - 3)(2x + 5) = 4x^2 + 4x - 15
\]
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Simplify this solution Mind Expander
To solve \( (2x-3)(2x+5) \), you can use the distributive property, often called the FOIL method for binomials. Multiplying the first terms gives \( 4x^2 \), then the outer terms \( 10x \), the inner terms \( -6x \), and finally the last terms \( -15 \). Combining all these, we get \( 4x^2 + 10x - 6x - 15 \), which simplifies to \( 4x^2 + 4x - 15 \). You now have the quadratic polynomial \( 4x^2 + 4x - 15 \). Want to take it a step further? You can factor it or find its roots using the quadratic formula! Factoring can often be easier, so keep an eye out for common factors!
