what is the product?\n$3x^{5}(2x^{2}+4x + 1)$\n$2x^{7}+4x^{6}+x^{5}$\n$6x^{10}+12x^{5}+3x^{5}$\n$6x^{7}+12x^{…

what is the product?\n$3x^{5}(2x^{2}+4x + 1)$\n$2x^{7}+4x^{6}+x^{5}$\n$6x^{10}+12x^{5}+3x^{5}$\n$6x^{7}+12x^{6}+3x^{5}$\n$3x^{5}+2x^{2}+4x + 1$

what is the product?\n$3x^{5}(2x^{2}+4x + 1)$\n$2x^{7}+4x^{6}+x^{5}$\n$6x^{10}+12x^{5}+3x^{5}$\n$6x^{7}+12x^{6}+3x^{5}$\n$3x^{5}+2x^{2}+4x + 1$

Answer

Explanation:

Step1: Apply distributive property

$3x^{5}(2x^{2}+4x + 1)=3x^{5}\times2x^{2}+3x^{5}\times4x+3x^{5}\times1$

Step2: Use exponent - rule for multiplication

For $3x^{5}\times2x^{2}$, when multiplying terms with the same base ($x$), we add the exponents. So $3x^{5}\times2x^{2}=(3\times2)x^{5 + 2}=6x^{7}$. For $3x^{5}\times4x=(3\times4)x^{5+1}=12x^{6}$, and $3x^{5}\times1 = 3x^{5}$.

Step3: Combine results

$3x^{5}\times2x^{2}+3x^{5}\times4x+3x^{5}\times1=6x^{7}+12x^{6}+3x^{5}$

Answer:

$6x^{7}+12x^{6}+3x^{5}$ (the third option)