Question

Question 15The expression, 81x^2 + bx + 36, is a perfect square trinomial.Give the value of b: Factor the expression as a perfect square:

Answer 1

We can factor a perfect square trinomial as a perfect square like this:

`A^2+2AB+B^2=(A+B)^2`

Now, we have to find the values of A and B in our trinomial: 81x^2+bx+36, by making it look like the general above general form.

As we can see:

`\begin{gathered} A^2+2AB+B^2=81x^2+bx+36 \\ \text{then:} \\ A^2=81x^2 \\ \text{then:} \\ A=\sqrt[]{81x^2}=\sqrt[]{81}*\sqrt[]{x^2}=9x \\ \text{And} \\ B^2=36 \\ \text{Then:} \\ B=\sqrt[]{36}=6 \end{gathered}`

Now we know that:

`\begin{gathered} bx=2* A* B=2*9x*6=2*9*6* x=108x \\ \text{then:} \\ (bx)/(x)=(108x)/(x) \\ b=108 \end{gathered}`

And, when we factor our perfect square trinomial as a perfect square it looks like this:

`(9x+6)^2`