Step 1a

Expanding the first term, we get:

2x(x) + 2x(4) - 3(x) - 3(4)

Simplifying further:

\$ 2x^2 + 8x - 3x - 12\$

Now, expanding the second term:

5(x + 2) = 5x + 5(2)

Simplifying: 5x + 10

Now let’s add the results of the first and second expansions:

\$ 2x^2 + 8x - 3x - 12 + 5x + 10 \$

Adding the like terms:

\$ 2x^2 + 10x - 2 \$

Explanation: We simplified the terms inside each bracket and then added similar terms together. This gave us the simple expression: \$ 2x^2 + 10x - 2 \$.

Step 2a

The given system of equations are
15x + 21y = 24 equation(1)
28y = -20x + 32 equation(2)

Explanation: Here the given system of equation are 15x + 21y = 24 and 28y = -21x + 32.

Step 2b

Let’s solve for y in terms of x from equation(2) \$y = (-20 x + 32)/(28)\$

Then simplify the above equation \$(-5x + 8) / 7\$

Explanation: Here the equation (2) is simplified in the y terms.

Step 2c

Now, let’s substitute this expression for y into equation(1) \$15x + 21(-5 x + 8/(7)​) = 24\$

Now, solve for x: \$15x - (105x)/(7) + (168)/7 = 24\$

Then simplify \$15x - 15x + 24 = 24\$

24 = 24

This equation doesn’t make sense, as it implies 24 = 24, which is always true. This indicates that the system of equations is dependent, meaning there are infinitely many solutions.

Explanation: Then here we plug the y value simplify the equation and then solve for the x value. It implies 24 = 24 so it gives many more infinitely solutions.