Simplify (4x-3)^2

Problem

(4⁢x−3)2 open paren 4 x minus 3 close paren squared

Solution

  1. Identify the expression as a binomial squared in the form (a−b)2 open paren a minus b close paren squared

  2. Apply the formula for the square of a binomial, which is (a−b)2=a2−2⁢a⁢b+b2 open paren a minus b close paren squared equals a squared minus 2 a b plus b squared

  3. Substitute a=4⁢x a equals 4 x and b=3 b equals 3 into the formula.

  4. Expand the terms by calculating (4⁢x)2 open paren 4 x close paren squared 2⁢(4⁢x)⁢(3) 2 times 4 x times 3 and 32 3 squared

a2=(4⁢x)2=16⁢x2 a squared equals open paren 4 x close paren squared equals 16 x squared

2⁢a⁢b=2⁢(4⁢x)⁢(3)=24⁢x 2 a b equals 2 times 4 x times 3 equals 24 x

b2=32=9 b squared equals 3 squared equals 9

  1. Combine the results to write the simplified expression.

Final Answer

(4⁢x−3)2=16⁢x2−24⁢x+9 open paren 4 x minus 3 close paren squared equals 16 x squared minus 24 x plus 9

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