Simplify (x)(20-2x)(20-2x)

Problem

x*(20−2*x)*(20−2*x)

Solution

1. Identify the expression as a product of a monomial and a squared binomial.

x*(20−2*x)2

2. Expand the squared binomial (20−2*x)2 using the formula (a−b)2=a2−2*a*b+b2

(20)2−2*(20)*(2*x)+(2*x)2

3. Simplify the terms inside the expansion.

400−80*x+4*x2

4. Distribute the x into the simplified trinomial.

x*(400−80*x+4*x2)

5. Multiply each term by x to find the final polynomial.

400*x−80*x2+4*x3

6. Rearrange the terms in descending order of their exponents.

4*x3−80*x2+400*x

Final Answer

x*(20−2*x)*(20−2*x)=4*x3−80*x2+400*x

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