Elijah used the distributive property to find the product of \(s(t)\) and \(h(t)\) . His work was marked incorrect. Explain Elijah's mistake. Correct Elijah's work to show the correct answer. \(s(t)\cdot h(t)=(4x-2)(5x-3)=20x^2-12x+10x+6=20x^2-2x+6\)
Elijah's mistake was in the step where he multiplied the terms \(10x\) and \(6\) together to obtain \(10x \cdot 6 = 60x\). Instead, he should have multiplied \(10x\) and \(6\) to obtain \(60x\), and then combined this term with the other two variable terms, \(-2x\) and \(20x^2\), resulting in \(20x^2 - 2x + 60x + 6\) (not \(20x^2 - 2x + 6\)).
To correct Elijah's work, we simplify this expression further by combining the like terms:
\(20x^2 - 2x + 60x + 6\)
\(= 20x^2 + 58x + 6\)
Therefore, the correct answer is \(20x^2 + 58x + 6\).