Answer:
<u><em>f(x) * g(x) is </em></u><u><em>8x^2 + 8x -6</em></u>
<u><em>f(x) - g(x) is </em></u><u><em>-2x + 5</em></u>
Step-by-step explanation:
<u><em>When finding the answer, we can notice they already give the values for the needed answers.</em></u>
<u><em>The first one requires f(x) and g(x). At the beginning of the question it shows that </em></u><u><em>f(x) is equal to 2x+3. Meaning we can plug in 2x+3 for f(x).</em></u>
<u><em>The same goes for g(x). At the begginning of the question, it shows that </em></u><u><em>g(x) is equal to 4x-2. Meaning we can plug in 4x-2 for g(x).</em></u>
<u><em>f(x) * g(x)</em></u>
<u><em>(2x+3) * (4x-2)</em></u>
<u><em>To find the answer, we need to </em></u><u><em>distibute the 2x+3 into 4x-2</em></u><u><em>.</em></u>
<u><em>To distribute, we do </em></u><u><em>:</em></u>
<u><em>2x * (4x-2) + 3 * (4x-2)</em></u>
<u><em>First we distribute the 2x</em></u>
<u><em>2x * 4x = 8x^2 and 2x * -2 = -4x</em></u>
<u><em>8x^2 - 4x</em></u>
<u><em>Next we distibute the 3</em></u>
<u><em>3 * 4x = 12x and 3 * -2 = -6</em></u>
<u><em>12x - 6</em></u>
<u><em>Now we can combine them by</em></u><u><em> adding like terms </em></u><u><em>to get the asnwer:</em></u>
<u><em>8x^2 = 8x^2</em></u>
<u><em>-4x + 12x = 8x</em></u>
<u><em>-6 = -6</em></u>
<u><em>The first answer is </em></u><u><em>8x^2 + 8x -6</em></u>
<u><em>Second question:</em></u>
<u><em>Since we already know the values for f(x) and g(x), all we have to do is </em></u><u><em>plug in the values</em></u><u><em>.</em></u>
<u><em>(2x+3) - (4x-2)</em></u>
<u><em>This time, since we are subtracting, all we have to do is </em></u><u><em>subtract like terms</em></u><u><em>.</em></u>
<u><em>2x - 4x = -2x</em></u>
<u><em>3 - (-2) = 5</em></u>
<u><em>The second answer is </em></u><u><em>-2x + 5</em></u>
