The problem is to expand the expression $(2x - 5)^2$.

AlgebraPolynomial ExpansionAlgebraic ManipulationBinomial Theorem
2025/4/27

1. Problem Description

The problem is to expand the expression (2x5)2(2x - 5)^2.

2. Solution Steps

We can expand the expression (2x5)2(2x - 5)^2 using the formula (ab)2=a22ab+b2(a - b)^2 = a^2 - 2ab + b^2.
In this case, a=2xa = 2x and b=5b = 5.
Applying the formula, we have:
(2x5)2=(2x)22(2x)(5)+(5)2(2x - 5)^2 = (2x)^2 - 2(2x)(5) + (5)^2
Now we simplify each term:
(2x)2=4x2(2x)^2 = 4x^2
2(2x)(5)=20x2(2x)(5) = 20x
(5)2=25(5)^2 = 25
Substituting these back into the equation:
(2x5)2=4x220x+25(2x - 5)^2 = 4x^2 - 20x + 25

3. Final Answer

4x220x+254x^2 - 20x + 25

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