Factoring a Perfect Square Trinomial

Factor $25 x^{2} + 20 x + 4.$

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
Notice that $25 x^{2}$ and $4$ are perfect squares because $25 x^{2} = {(5 x)}^{2}$ and $4 = 2^{2} .$ Then check to see if the middle term is twice the product of $5 x$ and $2.$ The middle term is, indeed, twice the product: $2 (5 x) (2) = 20 x .$ Therefore, the trinomial is a perfect square trinomial and can be written as ${(5 x + 2)}^{2} .$

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Factor $49 x^{2} - 14 x + 1.$

How did it go?