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h(n)=2n-2 g(n)=2n-5 F (gcdot h)(n) 4n^2+7n-15 4n^2-14n+10 9n^2-3n-2 4n^2+14n+10

Problemas

h(n)=2n-2
g(n)=2n-5
F (gcdot h)(n)
4n^2+7n-15
4n^2-14n+10
9n^2-3n-2
4n^2+14n+10

h(n)=2n-2 g(n)=2n-5 F (gcdot h)(n) 4n^2+7n-15 4n^2-14n+10 9n^2-3n-2 4n^2+14n+10

Solución

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María Elenaélite · Tutor durante 8 años
expert verifiedVerificación de expertos
4.0 (211 votos)

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To find \((g \cdot h)(n)\), we need to multiply the functions \(g(n)\) and \(h(n)\).<br /><br />Given:<br />\[ h(n) = 2n - 2 \]<br />\[ g(n) = 2n - 5 \]<br /><br />The product \((g \cdot h)(n)\) is:<br />\[ (g \cdot h)(n) = g(n) \cdot h(n) = (2n - 5)(2n - 2) \]<br /><br />Now, let's expand this expression:<br /><br />\[<br />(2n - 5)(2n - 2) = 2n \cdot 2n + 2n \cdot (-2) - 5 \cdot 2n - 5 \cdot (-2)<br />\]<br /><br />Calculating each term separately:<br />- \(2n \cdot 2n = 4n^2\)<br />- \(2n \cdot (-2) = -4n\)<br />- \(-5 \cdot 2n = -10n\)<br />- \(-5 \cdot (-2) = 10\)<br /><br />Combine all these terms:<br />\[ 4n^2 - 4n - 10n + 10 \]<br /><br />Simplify by combining like terms:<br />\[ 4n^2 - 14n + 10 \]<br /><br />Thus, the correct answer is:<br />\[ 4n^2 - 14n + 10 \]<br /><br />So, the correct option is:<br />\[ 4n^{2}-14n+10 \]
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