Expand Using the Binomial Theorem (2x-7)^2

Problem

(2*x−7)^2

Solution

1. Identify the components of the binomial expression (a+b)^n where a=2*x b=−7 and n=2

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

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

(2/0)(2*x)^2*(−7)^0+(2/1)(2*x)^1*(−7)^1+(2/2)(2*x)^0*(−7)^2)))

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

1⋅(2*x)^2⋅1+2⋅(2*x)⋅(−7)+1⋅1⋅(−7)^2

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

4*x^2−28*x+49

Final Answer

(2*x−7)^2=4*x^2−28*x+49

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