Factorize y² - 2xy - 3x
The confusing part of the question is the -3x
This is how far I went. y²- 2xy - 3x.
My solution so far. ( y + x ) ( y - 3x) , but expanding this will not give back the question. The - 3x is confusing. pls help
I suspect a typo.
- are you sure it wasn't
y^2 - 2xy - 3x^2 ?
then it would be
(y - 3x)(y + x)
To factorize the expression y² - 2xy - 3x, we need to look for common factors and factors that sum up or multiply to certain values.
First, let's try to find the common factors between the terms. In this case, there are no common factors, so we move on to the next step.
Next, let's look at the quadratic form of the expression. We have y² - 2xy - 3x, which can be written as y² - (2x)y - 3x.
Now, we need to find two numbers that multiply to give -3x and add up to give -2x, which is the coefficient of y in the expression.
To do this, we can break down -3x into two factors. The factors of -3x could be (-3x, 1), (x, -3), (-x, 3), (-x, 3), (3x, -1), or (1, -3x).
Considering these options, we can see that -3 and x are suitable factors. So the expression can be rewritten as:
y² - 3xy + xy - 3x
Now, we can group the terms:
(y² - 3xy) + (xy - 3x)
We can factor out the common terms from each group:
y(y - 3x) + x(y - 3x)
Now, notice that we have a common binomial factor of (y - 3x). We can factor that out:
(y - 3x)(y + x)
Therefore, the factored form of y² - 2xy - 3x is (y - 3x)(y + x).