the product of t decreased by 6 and 4 more than t

Let's translate the given expression into a mathematical expression:

- "The product of" indicates multiplication.
- "t decreased by 6" translates to \( t - 6 \).
- "4 more than t" translates to \( t + 4 \).

So, the expression for the product of \( t - 6 \) and \( t + 4 \) is:

\[
(t - 6)(t + 4)
\]

To expand this expression, we use the distributive property (also known as FOIL method for binomials):

\[
(t - 6)(t + 4) = t(t + 4) - 6(t + 4)
\]

Now, distribute \( t \) and \( -6 \) to each term in the second binomial:

\[
t^2 + 4t - 6t - 24
\]

Combine like terms:

\[
t^2 - 2t - 24
\]

So, the expanded form of the expression is:

\[
t^2 - 2t - 24
\]

Would you like any further explanation or have any questions?

Here are 5 related questions:
1. What would the expression be if it were the sum instead of the product of \( t-6 \) and \( t+4 \)?
2. How would the expression change if "t decreased by 6" were "t decreased by 8"?
3. What is the solution if the product equals zero?
4. Can you factor the expanded expression back into its original binomial factors?
5. How would the problem change if it involved the difference instead of the sum in the binomials?

**Tip:** When expanding binomials, carefully apply the distributive property to ensure all terms are correctly multiplied.

Learn how to expand and simplify the expression (t - 6)(t + 4) step-by-step. This problem covers algebraic concepts such as polynomial multiplication and the distributive property. Suitable for students in Grades 7-9.

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