We are given the following expression:
[tex]\mleft(x+3\mright)\mleft(2x^2+3x+7\mright)[/tex]We will use the distributive property:
[tex]\mleft(x+3\mright)\mleft(2x^2+3x+7\mright)=(x)(2x^2)+(x)(3x)+(x)(7)+(3)(2x^2)+(3)(3x)+(3)(7)[/tex]Solving the products:
[tex]\mleft(x+3\mright)\mleft(2x^2+3x+7\mright)=2x^3+3x^2+7x+6x^2+9x+21[/tex]Associating like terms:
[tex]\mleft(x+3\mright)\mleft(2x^2+3x+7\mright)=(2x^3)+(3x^2+6x^2)+(7x+9x)+21[/tex]Adding like terms:
[tex]\mleft(x+3\mright)\mleft(2x^2+3x+7\mright)=2x^3+9x^2+16x+21[/tex]Since we can't simplify any further this is the answer.
