Dylan uses the expressions (x2 – 2x + 8) and (2x2 + 5x – 7) to represent the length and width of his bedroom. Which expression represents the area (lw) of Dylan’s room?

isn't area = length x width ?

so ...

area = (x^2 - 2x + 8)(2x^2 + 5x - 7)

Length = 4 + x

Width = x
Height = x 2 + 1

What is the base area?

To find the area (lw) of Dylan's room, we need to multiply the length and width expressions together.

The length expression: x^2 - 2x + 8
The width expression: 2x^2 + 5x - 7

To find the area, we multiply these two expressions:

Area (lw) = (x^2 - 2x + 8) * (2x^2 + 5x - 7)

To simplify this expression, we can use the distributive property and combine like terms:

Area (lw) = 2x^4 + 5x^3 - 7x^2 - 4x^3 - 10x^2 + 14x + 16x^2 - 40x + 56

After combining like terms, the simplified expression for the area of Dylan's room is:

Area (lw) = 2x^4 + x^3 - 3x^2 - 26x + 56

To find the area of Dylan's room, we need to multiply the length and width of the room. Given that the length of the room is represented by the expression (x^2 – 2x + 8) and the width is represented by the expression (2x^2 + 5x – 7), we can multiply these two expressions to find the area.

When multiplying two expressions, we need to distribute each term of the first expression to every term in the second expression, and then combine like terms if any.

So, the area of Dylan's room can be found by multiplying (x^2 – 2x + 8) and (2x^2 + 5x – 7):

Area = (x^2 – 2x + 8) * (2x^2 + 5x – 7)

To multiply these expressions, we can use the distributive property and multiply each term individually:

Area = x^2 * 2x^2 + x^2 * 5x + x^2 * (-7) - 2x * 2x^2 - 2x * 5x - 2x * (-7) + 8 * 2x^2 + 8 * 5x + 8 * (-7)

Simplifying this expression by combining like terms gives us the final answer for the area:

Area = 2x^4 + 5x^3 - 7x^2 - 4x^3 - 10x^2 + 14x + 16x^2 + 40x - 56

Combining like terms further:

Area = 2x^4 + (5x^3 - 4x^3) + (-7x^2 - 10x^2 + 16x^2) + (14x + 40x) - 56

Area = 2x^4 + x^3 - x^2 + 54x - 56

Therefore, the expression 2x^4 + x^3 - x^2 + 54x - 56 represents the area (lw) of Dylan's room.