Simplify x(10-2x)(10-2x)

Problem

x*(10−2*x)*(10−2*x)

Solution

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

x*(10−2*x)2

2. Expand the squared binomial (10−2*x)*(10−2*x) using the FOIL method or the square of a binomial formula (a−b)2=a2−2*a*b+b2

(10)2−2*(10)*(2*x)+(2*x)2

3. Simplify the terms inside the expansion.

100−40*x+4*x2

4. Distribute the x outside the parentheses to every term inside the simplified expansion.

x(100)−x*(40*x)+x*(4*x2)

5. Combine the terms into a single polynomial, typically written in descending order of powers.

4*x3−40*x2+100*x

Final Answer

x*(10−2*x)*(10−2*x)=4*x3−40*x2+100*x

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