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El desarrollo de \( (4x+2)^{3} \) es \( 64x^{3}+96x^{2}+48x+8 \).
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Para desarrollar \( (4x+2)^{3} \), puedes usar la fórmula del binomio al cubo: \( (a + b)^{3} = a^{3} + 3a^{2}b + 3ab^{2} + b^{3} \). En este caso, \( a = 4x \) y \( b = 2 \). Por lo tanto, \( (4x + 2)^{3} = (4x)^{3} + 3(4x)^{2}(2) + 3(4x)(2^{2}) + (2)^{3} \). Calculando cada término, obtenemos: - \( (4x)^{3} = 64x^{3} \) - \( 3(4x)^{2}(2) = 3 \cdot 16x^{2} \cdot 2 = 96x^{2} \) - \( 3(4x)(2^{2}) = 3 \cdot 4x \cdot 4 = 48x \) - \( (2)^{3} = 8 \) Ahora, juntando todo: \[ (4x+2)^{3} = 64x^{3} + 96x^{2} + 48x + 8 \]
