Question

The length of the rectangle is x + 12. The width of the rectangle is x + 3. Please determine the area of the rectangle.

Show your work to receive full credit. You may show your work using the box method or you may show your work algebraically (distribution or FOIL). Make sure your answer is written in simplest standard form.


Simplify each expression. Show as much work as possible for each question for full credit. Write each answer in standard form.

a) (-5 +x)(x+4) (Show your work)
b) Is the product of -5 +x and x+4 equal to the product of 5+x and x-4? Explain your answer. (Show your work to prove your answer)
c) (2+5)(3²+4−3) (Show your work)

Answer 1

For part A, the product of (-5 + x)(x + 4) is equal to x^2 - x - 20. For part B, the product of -5 + x and x + 4 is not equal to the product of 5 + x and x - 4. And for part C the product of (3 + 5)(3^2 + 4 - 3) equals 70.

Explanation:

I will tell you how I came up with those answers.

The product of (-5 + x)(x + 4) can be found using the FOIL method(First, Outer, Inner, Last).

Start with multiplying -5 and x. -5 * x = -5x.

Now multiply -5 and 4. -5 * 4 = -20.

Next, multiply x and x. x * x = x^2.

Finally, multiply x and 4. x * 4 = 4x.

And now it is time to simplify and change to standard form.

-5x - 20 + x^2 + 4x.

x^2 - 5x - 20 + 4x.

x^2 - 5x + 4x - 20.

x^2 - x - 20.

The final answer for part A is x^2 - x - 20.

For part B, the product of -5 + x and x + 4 is already known.

But now we need to figure out the product of 5 + x and x - 4.

We can use the FOIL method again to solve for the new product.

Start by multiplying 5 and x. 5 * x = 5x.

Next, multiply 5 and -4. 5 * -4 = -20.

Now multiply x and x. x * x = x^2.

Finally, multiply x and -4. x * -4 = -4x.

And now we can simplify and arrange the terms into standard form.

5x - 20 + x^2 - 4x.

x^2 + 5x - 20 - 4x.

x^2 + 5x - 4x - 20.

x^2 + x - 20.

The final answer for part B is that the products of

(-5 + x)(x + 4) and (5 + x)(x - 4) are not equivalent. They look similar except the difference between them is the "x" value. The x value of the first equation's product is -x while the x value of the second equation's product is x.

For part C, use the FOIL method as used in the last questions to find the answer.

2 * 3^2 = 2 * 9 = 18.

2 * 4 = 8.

2 * -3 = -6.

5 * 3^2 = 5 * 9 = 45.

5 * 4 = 20.

5 * -3 = -15.

Now combine the numbers to get the final answer for part C.

Follow PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition and Subtraction).

The only operations are subtraction and addition. The rule is the add before subtracting, but this does not always apply. For this being true, we only need to perform the first operation from the left side.

18 + 8 - 6 + 45 + 20 - 15.

26 - 6 + 45 + 20 - 15.

20 + 45 + 20 - 15.

65 + 20 - 15.

85 - 15.

70.

So the last answer to part C is 70.

Also the area of the rectangle is x^2 + 15x + 36. I forgot that part, my apologies.