\(4x^{2}+25-20x\) can be expressed as the square of:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(2x-5\)
Arrange the terms as \(4x^{2}-20x+25\) and compare with \((a-b)^{2}=a^{2}-2ab+b^{2}\). Here \(4x^{2}=(2x)^{2}\) and \(25=5^{2}\), and the middle term \(-20x\) is \(-2\times2x\times5\), so the minus sign goes between them.
\(4x^{2}-20x+25=(2x)^{2}-2(2x)(5)+5^{2}=\) \((2x-5)^{2}\)
Why the other options are incorrect
Option (1) \(\displaystyle 2x-\frac{5}{2}\) — Incorrect. Its square is \(\displaystyle 4x^{2}-10x+\frac{25}{4}\): the middle and the last terms do not match.
Option (2) \(-2x-5\) — Incorrect. Its square equals \((2x+5)^{2}=4x^{2}+20x+25\), with a plus middle term.
Option (4) \(2x+5\) — Incorrect. Its square is \(4x^{2}+20x+25\), again with a plus middle term.