Question

Multiply (8+12t)(-3-6t)

Answer 1

`\boxed{\mathtt{-72t^(2)-84t-24}}`

Explanation:

`\textsf{We are asked to \underline{multiply} the given expression.}\\`

`\textsf{We should use the \underline{FOIL Method.}}`

`\Large\underline{\textsf{What is the FOIL Method?}}`

`\textsf{The \underline{FOIL Method} is a method used to \underline{multiply 2 binomials together}.}`

`\large\underline{\textsf{Foil Means:}}`

`\textsf{Fronts - Front x Front.}`

`\textsf{Outsides - Front x Inside.}`

`\textsf{Insides - Inside x Front.}`

`\textsf{Lasts - Inside x Inside.}`

`\mathtt{(4x-3x)(5x-6x)}`

`\textsf{4x - First front.}\\\textsf{-3x - First inside.}\\\textsf{5x - Second front.}\\\textsf{-6x - Second inside.}`

`\large\underline{\textsf{Multiply using the FOIL Method:}}`

`\mathtt{(8+12t)(-3-6t)}\\`

`\mathtt{(8 * -3)+(8 * -6t) + (12t * -3) +( 12t * -6t)}`

`\mathtt{-24+ -48t -36t-72t^(2)}`

`\large\underline{\textsf{Combine Like Terms:}}`

`\boxed{\mathtt{-72t^(2)-84t-24}}`

Answer 2

to multiply (8+12t)(-3-6t), we can use the distributive property and then simplify:

(8+12t)(-3-6t)

= 8(-3) + 8(-6t) + 12t(-3) + 12t(-6t)

= -24 - 48t - 36t + (-72t^2)

= -72t^2 - 84t - 24

Therefore, (8+12t)(-3-6t) = -72t^2 - 84t - 24.

Explanation: