I’m working on factoring trinomials of the form ax2 + bx + c & perfect square trinomials. This chapter explains that a further method will be needed to conduct a trial and check process, in which the middle term is the sum of the products.
Here’s the problem as follows:
4y2 - 20y + 25 = (2y-5) ( )
You need another 2y to get 4y
4y2 - 20y + 25 = (2y-5) (2y )
now that-5*2y = -10y
so the product of -5 and the last term must be 25 so -5
so
(2y-5)(2y-5)
To factor the trinomial 4y^2 - 20y + 25, we can use a method called trial and check. In this method, we find two binomials that when multiplied together, give us the original trinomial.
Let's start by looking at the first term, 4y^2. We want to find two binomials that when multiplied, give us this term. The only way to obtain 4y^2 is by multiplying 2y with 2y.
Next, we look at the last term, 25. We want to find two binomials that when multiplied, give us this term. The only way to obtain 25 is by multiplying 5 with 5.
Now, we need to determine the signs of these binomials to make them add up to the middle term, -20y. Since the middle term is negative, we need to have one negative and one positive term.
Putting it all together, we have:
4y^2 - 20y + 25 = (2y - 5)(2y - 5)
Notice that both binomials are the same because the original trinomial is a perfect square trinomial. Therefore, the factored form of the trinomial is:
4y^2 - 20y + 25 = (2y - 5)^2