Answer:
(5x + 3)² + 3
Explanation:
25x² + 30x + 12 =
= (25x² + 30x) + 12
How do we make 25x² + 30x into a perfect square?
25x² is the square of 5x, so our binomial that is squared will start with
(5x + ___)²
We need to find the number that is added to 5x inside the parentheses.
The middle term of the squared binomial is 2 times the first term times the second term.
2(5x)b = 30x
b = 3
The binomial is (5x + 3).
When we square it, the last term will be 9. We need to add 9 to 25x² + 30x to have a perfect square. Then we also need to subtract 9 to not change the value of the expression.
= (25x² + 30x + 9) + 12 - 9
= (5x + 3)² + 3