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.

Question

s(t)*h(t)=(4x-2)(5x-3)
=20x^2 - 12x+10x+6
=20x^2-2x+6

explain your answer and show how you got it

Answer 1

Elijah's mistake was in the second step where he incorrectly combined the middle terms of -12x and 10x as -2x.

The correct way to multiply (4x-2) and (5x-3) using the distributive property is as follows:

s(t)*h(t)=(4x-2)(5x-3)
= 4x*(5x) + 4x*(-3) - 2*(5x) - 2*(-3)
= 20x^2 - 12x - 10x + 6
= 20x^2 - 22x + 6

Therefore, the correct product of s(t) and h(t) is 20x^2 - 22x + 6.