Question

Simplify the expressions below. Write the final product in standard form and show your work to receive full credit.

1. 2x4(4x2 + 3x + 1)
2. (4x – 3)(2x2 – 7x + 1)
3. (x2 + 4x – 3)(2x2 + x + 6)
4. Write a simplified polynomial expression to represent the area of the rectangle below.

Picture of rectangular with one side labeled as 2 times x minus 4 and another side labeled as x plus 5
5. Write a simplified polynomial expression to represent the area of the square tile, shown below.

A square shaped tile with length x minus three is shown.
Pictures in respo

Answer 1

1. \[8x^6 + 6x^5 + 2x^4\]
2.\[8x^3 -28x^2 + 4x -6x^2 + 21x - 3\]
\[= 8x^3-34x^2 + 25x -3\]
3. \[2x^4 + x^3+6x^2 +8x^3+4x^2+24x-6x^2 - 3x - 18\]
\[= 2x^4+9x^3 +4x^2+21x-18\]

Answer 2

Area of Rectangle = First Side*Other Side or Length*Breadth

Therefore, Required Polynomial = 2*(x - 4)*(x + 5)
\[= 2(x^2 + 5x -4x -20)\]
\[= 2x^2 + 2x - 40\] is the required expression..

Answer 3

5. Area of square : Length*Length
\[= (x-3)^2 = x^2 + 9 -6x\] is the required expression..

Answer 4

@waterineyes you are correct about 5., but if it were in Standard Form, the answer would be \[x^{2}-6x + 9\]

Answer 5

Question asks for simplified expression.
Don't you think my way of writing is more simplified than yours?? :P