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An open top box is formed by cutting squares out of a 5 inch by 7 inch piece of paper and then folding up the sides. The volume V(x) in cubic inches of this type of open-top box is a function of the side length x in inches of the square cutouts and can be given by V(x)=(7-2x)(5-2x)(x). Rewrite this equation by expanding the polynomial.

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MrRoyal

Answer:

[tex]V(x) = 4x^3 - 24x^2+35x[/tex]

Step-by-step explanation:

Given

[tex]V(x) = (7 - 2x)(5 - 2x)(x)[/tex]

Required

Expand the expression

[tex]V(x) = (7 - 2x)(5 - 2x)x[/tex]

Expand bracket

[tex]V(x) = (7 - 2x)(5 * x - 2x * x)[/tex]

[tex]V(x) = (7 - 2x)(5x - 2x^2)[/tex]

Further expand bracket

[tex]V(x) = 7(5x - 2x^2) - 2x(5x - 2x^2)[/tex]

[tex]V(x) = 35x - 14x^2 - 10x^2 + 4x^3[/tex]

[tex]V(x) = 35x - 24x^2 + 4x^3[/tex]

[tex]V(x) = 4x^3 - 24x^2+35x[/tex]

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