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?

2x⁴+x³-x²+54x+56

Step-by-step explanation:

Given the expression length of dylan room =  (x² – 2x + 8) and width = (2x² + 5x – 7), assuming the shap of the room is rectangular in nature, the formula for calculating area of a triangle is given as;

Area of rectangle = Length *Width

Area of the rectangle =  (x² – 2x + 8)(2x² + 5x – 7)

Area of the rectangle  = x²(2x² + 5x – 7) - 2x (2x² + 5x – 7) + 8(2x² + 5x – 7)

= (2x⁴+5x³-7x²)-(4x³+10x²-14x)+(16x²+40x-56)

expanding the bracket

= 2x⁴+5x³-7x²-4x³-10x²+14x+16x²+40x-56

Collecting the like terms;

= 2x⁴+5x³-4x³-7x²-10x²+16x²+40x+14x+56

= 2x⁴+x³-x²+54x+56

Hence, the expression that represents the area (lw) of Dylan's room is 2x⁴+x³-x²+54x+56

0.02040816326