Write as a square of a binomial.
4.8xy + 36y^2 + 0.16x^2
What nonsense and gibberish by the bot..
4.8xy + 36y^2 + 0.16x^2
= .16(225y^2 + 30xy + x^2)
= .16(15y + x)^2
or
= ( .4(15y + x) )^2
or
= ( 6y + .4x)^2
To write it as a square of a binomial, we need to find two terms that square to give us the given expression. We can try to identify a pattern in the expressions 4.8xy and 36y^2.
4.8xy can be factored as 2.4x * y * 2, while 36y^2 can be factored as 6y * 6y. Notice that the sum of the first and last term in this factorization is 2.4x * y + 6y = 2.4y(x+2.5).
If we square this sum, we get:
(2.4y(x+2.5))^2 = (2.4y)^2 * (x+2.5)^2
= 5.76y^2 * (x+2.5)^2
Now, we need to show that 0.16x^2 can be written as some constant multiplied by (x+2.5)^2. This is relatively easy to do:
0.16x^2 = 0.4 * 0.4x^2
= 0.4 * (x+0)^2
Putting these pieces together, we get:
4.8xy + 36y^2 + 0.16x^2 = 5.76y^2 * (x+2.5)^2 + 0.4 * (x+0)^2
Therefore, the given expression can be written as the square of the binomial:
(2.4y(x+2.5) + 0.2x)^2.