Question

16x^2 + 56x + 49 Is this a special product? If yes, what type

Answer 1

Let's check if the given equation is a special product.

`16x^2+56x+49`

Let,

a = 1st term coefficien

b = 2nd term coefficient

c = constant

We get,

a = 16

b = 56

c = 49

Let's check, you can use this method to check if it is a perfect square binomial:

`\begin{gathered} \text{ 2(}\sqrt[]{a}\text{ x }\sqrt[]{c})\text{ = b ;} \\ (a+c)^2\text{ if b is positive} \\ (a-c)^2\text{ if b is negative} \end{gathered}`
`\begin{gathered} 2(\sqrt[]{16}\text{ x }\sqrt[]{49})\text{ = 56} \\ 2(4\text{ x 7) = 56 ; since b is positive, a and c are positive} \\ 2(28)\text{ = 56} \\ 56\text{ = 56} \end{gathered}`

Therefore, the equation is a special product. It is a square of a binomial.

The answer is YES, it is a special product. It is a Square of a Binomial (x + y)².