Factorise the quadratic $4 x^{2} - 20 x + 25$

medium 3 marks Class 8 · Mathematics · Algebraic Expressions and Identities

Answer

(2x - 5)^2

The correct answer is (2x - 5)^2 — Thus the quadratic factors as a square of a binomial.

Step-by-step solution

Observe that $4 x^{2}$ is $(2 x)^{2}$ , $25$ is $5^{2}$ , and $- 20 x$ equals $2 \times (2 x) \times 5 = 2 ab$ .
Recognise it as a perfect square trinomial.
Write the factorisation as $(2 x - 5) (2 x - 5)$ .
Simplify to $(2 x - 5)^{2}$ .
Thus the quadratic factors as a square of a binomial.

Common mistake: Treating it as a difference of squares

Concept tested: Factoring perfect square trinomials