Question

Jamie used the distributive property to find the product of s(t) and h(t).

His work was marked incorrect. Identify Jamie's mistake. What advice
would you give Jamie to avoid this mistake in the future?
SCt).h(t)= (3x-4)(2x-8)
= 6X2 -24x-8x - 32
= 6x2 -32% - 32

Answer 1

Jamie's mistake: The last term
`32` and not
`-32`. Jamie multiply the signs incorrectly.

Advice to avoid this mistake in the future: Jamie should remember that when two negative numbers are multiplied, the result is a positive number.

Explanation:

The correct procedure is the one shown below:

`=(3x-4)(2x-8)\\\\=(3x)(2x)+(3x)(-8)+(-4)(2x)+(-4)(-8)\\\\=6x^2-24x-8x+32\\\\=6x^2-32x+32`

You can identify that the last term is actually
`32` and not
`-32`, so Jamie multiply the signs incorrectly.

To avoid that mistake in the future, Jamie must remember the mulitplication of signs:

`(+)(+)=+\\(-)(-)=+\\(-)(+)=-\\(+)(-)=-`

So when two negative numbers are multiplied, the result is a positive number.