# Chapter 4 - Polynomials - 4.5 Multiplication of Polynomials - 4.5 Exercise Set: 62

$3t^3-19t^2+23t-4$

#### Work Step by Step

Using the Distributive Property, the product of the given expression, $(3t-4)(t^2-5t+1) ,$ is \begin{array}{l}\require{cancel} 3t(t^2)+3t(-5t)+3t(1)-4(t^2)-4(-5t)-4(1) \\\\= 3t^3-15t^2+3t-4t^2+20t-4 \\\\= 3t^3+(-15t^2-4t^2)+(3t+20t)-4 \\\\= 3t^3-19t^2+23t-4 .\end{array}

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