Maths-
General
Easy

Question

The dimensions of a rectangle are shown. Write the area of the rectangle as a sum of cubes .

The correct answer is: Thus, the sum of cubes are of the form x^3 + 3^3.


    ANSWER:
    Hint:
    open parentheses straight a cubed plus straight b cubed close parentheses equals left parenthesis straight a plus straight b right parenthesis open parentheses straight a squared minus ab plus straight b squared close parentheseswhere a and b can be real values, variables or multiples of both.
    We are asked to write the area of the rectangle as the sum of cubes
    Step 1 of 2:
    The length of the rectangle is: x2- 3x + 9
    The width of the rectangle is: (x + 3)
    Thus, the area of the rectangle is:
    straight A equals lw
    equals left parenthesis x plus 3 right parenthesis open parentheses x squared minus 3 x plus 9 close parentheses
    Step 2 of 2:
    Analyze the area of the rectangle, we get:
    left parenthesis straight x plus 3 right parenthesis open parentheses straight x squared minus 3 straight x plus 9 close parentheses equals straight x cubed plus 3 cubed comma text  where  end text straight x equals straight x straight & straight y equals 3
    Thus, the sum of cubes are of the form x3 + 33
    Note:
    The area of a rectangle with length l and width w is  A = lw.

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