Answer:
[tex]f(x)*g(x) = x^2+3x-28[/tex]
Step-by-step explanation:
[tex]f(x) = x+7\\g(x) = x-4\\\\f(x) * g(x) = (x+7) * (x-4)[/tex]
To solve a multiplication of 2 parenthesis, we'll multiply each of the terms on the left with each of the terms on the right. Then, add all of the products together.
First, x (left) with x (right):
[tex]x * x = x^2[/tex]
Next, x (left) with -4 (right):
[tex]x * (-4) = -4x[/tex]
Next, 7 (left) with x (right):
[tex]7 * x = 7x[/tex]
Finally, 7 (left) with -4 (right):
[tex]7 * (-4) = -28[/tex]
Now we have 4 products. To find the result of the entire expression, we need to add all of these together.
[tex]x^2 - 4x + 7x - 28[/tex]
We can simplify -4x+7x to 3x:
[tex]x^2 + 3x-28[/tex]
Answer: [tex]f(x)*g(x) = x^2+3x-28[/tex]
