Perfect Square Trinomial Formula

An expression obtained from the square of binomial equation is a perfect square trinomial. If a trinomial is in the form ax2 + bx + c is said to be perfect square, if only it satisfies the condition b2 = 4ac.

The Perfect Square Trinomial Formula is given as,

\[\large (ax)^{2}+2abx+b^{2}=(ax+b)^{2}\]

\[\large (ax)^{2}-2abx+b^{2}=(ax-b)^{2}\]

Solved Examples

Question: Is the trinomial x2 – 6x + 9 a perfect square?


x2 – 6x + 9
= x2 – 3x – 3x + 9
= x(x – 3) – 3(x – 3)
= (x – 3)(x – 3)

The factors of the given equation are a perfect square.

So, the trinomial is a perfect square.

Practise This Question

Which of the following statements is/are correct for hydrophily?

(i) Pollination by water is rare in flowering plants and is limited mostly to monocotyledons.

(ii) In majority of aquatic plants such as water hyacinth and water lily pollination takes place by insects and wind

(iii) In most of the water pollinated species pollen grains are protected from wetting by a mucilaginous covering.

(iv) In Vallisneria, female flowers reach the surface of water and receive the pollen grains, whereas in Zostera, female flowers remain submerged and receive pollen grains under water.