Factor 25x2-20x+4 I can't figure out what to do with 25.
I assume you mean
25 x^2 - 20 x + 4
factors of 25
1,25
5, 5
factors of 4
1,4
2,2
well 5*2 = 10 and two of those is 20
so try
(5 x - 2)(5 x - 2)
To factor the expression 25x^2 - 20x + 4, we need to find two binomials that, when multiplied together, give us the original expression.
First, let's look at the coefficient of the x^2 term, which is 25. We can start by breaking it down into its prime factors. In this case, since 25 is already a perfect square, it breaks down to 5 × 5 or 5^2.
So we can rewrite the expression as (5x)^2 - 20x + 4.
Now, let's focus on the last term, which is 4. We need to find two numbers that multiply together to give us 4. In this case, we have 2 × 2 or 2^2.
Thus, we can rewrite the expression as (5x)^2 - 20x + 2^2.
Next, let's find the middle term, -20x. We need to split this term in such a way that it combines with the other parts of the expression.
Since -20x is a result of multiplying -4 and 5x, we can rewrite the expression as (5x)^2 - 4(5x) + 2^2.
Now we have three terms: (5x)^2, -4(5x), and 2^2.
To factor this expression completely, we can use a method called grouping. We group the first two terms and the last two terms:
[(5x)^2 - 4(5x)] + 2^2.
Now we can factor out the common terms from each group:
5x(5x - 4) + 2^2.
Simplifying further, we get:
5x(5x - 4) + 4.
Therefore, the fully factored form of the expression 25x^2 - 20x + 4 is 5x(5x - 4) + 4.