Answer:
w⁴+5w³+17w²+24w +18
Step-by-step explanation:
Area of a rectangle = length * width
Given
Length = w²+3w+9
width = w²+2w+2
Area of the rectangle = (w²+3w+9)(w²+2w+2)
Area of the rectangle = w²(w²) + 2w(w²) + 2w² + 3w(w²) + 3w(2w) + 2(3w)+9w²+9(2w)+9(2)
Area of the rectangle = w^4+2w^3+2w²+3w^3+6w^2+6w+9w²+18w+18
Collect the like terms;
Area of the rectangle = w^4+2w^3+3w^3+2w²+6w²+9w²+6w+18w+18
Area of the rectangle = w⁴+5w³+17w²+24w +18
Hence the area of the entire triangle is w⁴+5w³+17w²+24w +18
