Telangana TET Paper 1 Exam Model Paper 4

Concept:Recognize each quadratic as a perfect square trinomial: $a^2 \pm 2ab + b^2 = (a \pm b)^2$.Explanation:First, factor $x^2 - 14x + 49$. Notice it matches $(x)^2 - 2(x)(7) + 7^2$, so it equals $(x - 7)^2$.Next, factor $x^2 + 6x + 9$. It matches $(x)^2 + 2(x)(3) + 3^2$, so it equals $(x + 3)^2$.The given expression is the product of these two squares: $(x - 7)^2 (x + 3)^2$.Take the square root of the whole product: $\sqrt{(x - 7)^2 (x + 3)^2} = (x - 7)(x + 3)$.Thus the square root simplifies directly to the product of the two binomials.Answer:A. $(x - 7)(x + 3)$