factor 9x^2-6x+1
To factor 9x^2 - 6x + 1, we need to find two binomials that multiply together to give us the original expression.
We can start by looking at the first term, 9x^2, which can be factored as (3x)^2.
Next, we look at the last term, 1, which has only one possible combination, (1)(1).
Now, we need to find two numbers that multiply together to give us the middle term, -6x, while also considering the factors we found above.
Since 2 multiplied by 3 is 6, and -2 multiplied by -3 is also 6, we can choose -2 and -3 as our middle term factors.
Putting it all together, we have:
(3x - 1)(3x - 1)
Simplifying further, we can write it as:
(3x - 1)^2
To factor the expression 9x^2 - 6x + 1, follow these steps:
Step 1: Check if the expression can be factored further by using the quadratic formula or completing the square. In this case, we can proceed with factoring.
Step 2: Look for two numbers that multiply to give the product of the coefficient of x^2 term (9) and the constant term (1), which is 9 * 1 = 9.
Step 3: Find two numbers that add up to give the coefficient of the x term (-6). This can be -3 and -3, because -3 + -3 = -6.
Step 4: Rewrite the expression by splitting the middle term (-6x) into -3x and -3x.
9x^2 - 6x + 1 can be written as:
(9x^2 - 3x) + (-3x + 1)
Step 5: Factor out the greatest common factor for each pair of terms.
3x * (3x - 1) + (-1) * (3x - 1)
Step 6: Combine like terms.
(3x - 1) * (3x - 1)
Step 7: Simplify the expression.
(3x - 1)^2
Therefore, the factored form of 9x^2 - 6x + 1 is (3x - 1)^2.