x^2+8x complete the square to make the binomial a perfect trinomial
We have:
(a+b)^2 = a^2 + 2 a b + b^2
So, if we want the a^2 term is this identity to represent x^2, then the
2 a b term should be 8x. This means that b should be 4. Let's see what happens if we put a = x and b = 4:
(x+4)^2 = x^2 + 8 x + 16
So, we see that:
x^2 + 8 x = (x+4)^2 - 16
To complete the square and make the binomial x^2 + 8x a perfect trinomial, you can follow these steps:
1. Take half of the coefficient of the x-term (8) and square it: (8/2)^2 = 16.
2. Add the squared value obtained in step 1 to both sides of the equation. This maintains the equation's balance.
x^2 + 8x + 16 = x^2 + 8x + 16
3. Factor the perfect square trinomial on the left side, and simplify the right side of the equation:
(x + 4)^2 = x^2 + 8x + 16
4. Now, the binomial on the left side is a perfect trinomial since it can be expressed as the square of (x + 4).