Algebra

What is the coefficient of x^2 in (x^3 + x^2 + x + 1)(x^4 + 3x^3 + 8x + 7x + 1)?    

                                (x³ + x² + x + 1)(x⁴ + 3x³ + 8x² + 7x + 1)    I think you left off that exponent.  

                                                          x² • 1   =   x²     

                                                          x • 7x   =  7x²      

                                                         1 • 8x²  =  8x²     

add them up                                                    16x²     

_.   

When we expand the product, we get $x^7 + 4x^6 + 4x^5 + 19x^4 + 16x^2 + 16x + 1.$ We see that the coefficient of $x^2$ is $16$.