Question

25x^2 - 10xy+y^2- 9 ​

Answer 1

Разложение на множители:

$25x^2-10xy+y^2-9=(5x-y)^2-3^2=\\\\=(5x-y-3)(5x-y+3)$

Answer 2

$25 {x}^{2} - 10xy + {y}^{2} - 9 = (5x - y)^{2} - 9$

Answer 3

The expression you've given is a quadratic expression in two variables, x and y:

25x^2 - 10xy + y^2 - 9

This expression can be factored as a quadratic trinomial. To factor it, we look for two binomials that, when multiplied together, give us the original expression. The factors of this expression can be found by considering the middle term (-10xy) as the result of multiplying two terms in the form of (ax + by):

(5x - y)(5x - y) - 9

Now, if we expand the above expression using the distributive property, we can see that it matches the original expression:

(5x - y)(5x - y) = 25x^2 - 10xy + y^2

So, the factored form of the expression is:

(5x - y)^2 - 9

You can leave it in this factored form, or if you want to simplify it further, you can recognize that this is the difference of squares and factor it as follows:

[(5x - y) + 3][(5x - y) - 3]

So, the fully factored expression is:

(5x - y + 3)(5x - y - 3)