Evaluate g(p)h(p) by modeling or by using the distributive property.g(p) = (p - 2) and h(p) = (p3 + 4p2 – 2)

Answer:g(p)h(p) = = p^4 + 2p^3 - 8p^2 -2p + 4Step-by-step explanation:Hello!We will use the distributive property:g(p) h(p) = ( p - 2 ) * ( p^3 + 4p^2 - 2 ) = ( p^3 + 4p^2 - 2 ) * ( p - 2 ) The distributive property allow us to multiply the first term (p^3 + 4p^2 - 2) by every member of the second member, that is p and -2.g(p) h(p) = ( p^3 + 4p^2 - 2 ) * p + ( p^3 + 4p^2 - 2 ) * (-2)Now we can do the same for the two resulting terms, that is, we can multiply every term in parenthesis ( p^3 + 4p^2 - 2 ) by the term on the rigth:( p^3 + 4p^2 - 2 ) * p = (p^3)*p + (4p^2)*p - 2*p = p^4 + 4p^3 -2p( p^3 + 4p^2 - 2 ) * (-2) = (p^3)*(-2) + (4p^2)*(-2)- 2*(-2) = -2p^3 - 8p^2 + 4And now we can sum both terms and add monomials with the same exponent of t. Look at the underlined terms g(p) h(p) = p^4 + 4p^3 -2p - 2p^3 - 8p^2 + 4 = p^4 +2p^3 -2p - 8p^2 + 4               = p^4 + 2p^3 - 8p^2 -2p + 4