Find the product. Collect all like terms. (t+3)(t+4)

1. Distribute the terms: We need to multiply the two binomials $(t+3)$ and $(t+4)$. We can use the FOIL method (First, Outer, Inner, Last) or simply distribute each term in the first binomial to each term in the second binomial.

$$(t+3)(t+4) = t(t+4) + 3(t+4)$$

1. Perform the multiplication: Now, distribute $t$ to $(t+4)$ and $3$ to $(t+4)$.

$$t \times t + t \times 4 + 3 \times t + 3 \times 4$$

$$t^2 + 4t + 3t + 12$$

1. Collect like terms: Identify terms that have the same variable raised to the same power. In this expression, $4t$ and $3t$ are like terms.

$$t^2 + (4t + 3t) + 12$$

1. Combine like terms: Add the coefficients of the like terms.

$$t^2 + 7t + 12$$