Expand Using the Binomial Theorem (5x-4)^2

Problem

(5*x−4)2

Solution

1. Identify the terms of the binomial (a+b)n where a=5*x b=−4 and n=2

2. Apply the Binomial Theorem formula, which states (a+b)n=(∑_k=0^n)((n/k))*a(n−k)*bk)

3. Write the expansion by substituting the values into the formula for k=0,1,2

(2/0)(5*x)2*(−4)0+(2/1)(5*x)1*(−4)1+(2/2)(5*x)0*(−4)2)))

4. Calculate the coefficients using the combination formula (n/k))

1⋅(5*x)2⋅1+2⋅(5*x)⋅(−4)+1⋅1⋅(−4)2

5. Simplify each term by squaring the constants and variables.

25*x2−40*x+16

Final Answer

(5*x−4)2=25*x2−40*x+16

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