Please provide solutions for the following questions: 2.3, 7.3, 7.3.1, and 8.2.

Question

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Here are the solutions to the remaining questions:

2.3) A factor produces 1280 boxes in 8 days. How many boxes are produced in 28 days?

Calculate the production rate per day.
$\text{Rate} = \frac{1280 \text{ boxes}}{8 \text{ days}} = 160 \text{ boxes/day}$
Calculate the total boxes produced in 28 days.
$\text{Total boxes} = 160 \text{ boxes/day} \times 28 \text{ days} = 4480 \text{ boxes}$
The factory produces $\boxed{\text{4480 boxes}}$ in 28 days.

7.3) Expand $3(x+2)^2$
Expand the squared term $(x+2)^2$ .
$(x+2)^2 = x^2 + 2(x)(2) + 2^2 = x^2 + 4x + 4$
Multiply the result by 3.
$3(x^2 + 4x + 4) = 3x^2 + 12x + 12$
The expanded expression is $\boxed{3x^2 + 12x + 12}$ .

7.3.1) Simplify $\frac{x^2-9}{x^2-3x}$
Factor the numerator using the difference of squares formula ( $a^2 - b^2 = (a-b)(a+b)$ ).
$x^2 - 9 = x^2 - 3^2 = (x-3)(x+3)$
Factor the denominator by taking out the common factor $x$ .
$x^2 - 3x = x(x-3)$
Substitute the factored expressions back into the fraction and simplify by canceling common factors.
$\frac{x^2-9}{x^2-3x} = \frac{(x-3)(x+3)}{x(x-3)} = \frac{x+3}{x}$
The simplified expression is $\boxed{\frac{x+3}{x}}$ .

8.2) A number is multiply by 7 and then decrease by 12. The result is 23. Write and solve an equation to find the number.
Let the unknown number be $x$ .
Write the equation based on the problem description.
$7x - 12 = 23$
Solve the equation for $x$ .
$7x - 12 = 23$ $7x = 23 + 12$ $7x = 35$ $x = \frac{35}{7}$ $x = 5$
The number is $\boxed{5}$ .

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