Answer :
Final answer:
To find the area of the given polynomial multiplied by the height, we need to distribute the height to each term and simplify the expression. The final expression for the area is 80x^6 - 226x^5 - 428x^4 + 426x^3 - 1000x^2 - 140x + 490.
Explanation:
The given expression can be written as a polynomial in the form ax³ + bx² + cx + dx + e, where a = 20, b = -23, c = -41, d = 35, e = 40, and f = -70.
To find the area of the polynomial multiplied by the height, we need to multiply each term of the polynomial by the height and add them up. So, the area is (20x^5)(4x-7) + (-23x^4)(4x-7) + (-41x^3)(4x-7) + (35x^2)(4x-7) + (40x)(4x-7) + (-70)(4x-7).
We can simplify this expression by distributing the height to each term and combining like terms. The final expression for the area is 80x^6 - 226x^5 - 428x^4 + 426x^3 - 1000x^2 - 140x + 490.
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