Certainly! Let's simplify the expression [tex]\((2x - 3)^2\)[/tex] step-by-step.
Step 1: Write the expression in the expanded form of a square of a binomial.
[tex]\[
(2x - 3)^2 = (2x - 3)(2x - 3)
\][/tex]
Step 2: Use the distributive property (also known as the FOIL method for binomials) to expand the expression.
[tex]\[
(2x - 3)(2x - 3) = 2x \cdot 2x + 2x \cdot (-3) + (-3) \cdot 2x + (-3) \cdot (-3)
\][/tex]
Step 3: Multiply each pair of terms.
[tex]\[
2x \cdot 2x = 4x^2
\][/tex]
[tex]\[
2x \cdot (-3) = -6x
\][/tex]
[tex]\[
(-3) \cdot 2x = -6x
\][/tex]
[tex]\[
(-3) \cdot (-3) = 9
\][/tex]
Step 4: Combine the results from the multiplications.
[tex]\[
(2x - 3)^2 = 4x^2 - 6x - 6x + 9
\][/tex]
Step 5: Combine like terms.
[tex]\[
4x^2 - 6x - 6x + 9 = 4x^2 - 12x + 9
\][/tex]
Thus, the simplified expression is:
[tex]\[
(2x - 3)^2 = 4x^2 - 12x + 9
\][/tex]
So, the answer is:
\[
4x^2 - 12x + 9
\
