• A trinomial that is a perfect square has two forms:

a² + 2ab + b² = (a + b)²

a² − 2ab + b² = (a − b)²

• To recognise it, check that the first and last terms are perfect squares and that the middle term equals twice the product of the two roots.
• For example, in x² + 10x + 25 the first term is x², 25 = 5², and 10x = 2 × x × 5.
• So x² + 10x + 25 = (x + 5)².