Simplify (x)(22-2x)(22-2x)

Problem

x*(22−2*x)*(22−2*x)

Solution

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

x*(22−2*x)2

2. Expand the squared binomial (22−2*x)2 using the formula (a−b)2=a2−2*a*b+b2

(22)2−2*(22)*(2*x)+(2*x)2

3. Simplify the terms inside the parentheses.

484−88*x+4*x2

4. Distribute the x into each term of the simplified quadratic expression.

x(484)−x*(88*x)+x*(4*x2)

5. Reorder the terms in descending order of their exponents to write the polynomial in standard form.

4*x3−88*x2+484*x

Final Answer

x*(22−2*x)*(22−2*x)=4*x3−88*x2+484*x

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