Question

СРОЧНО! 6) a^2 - 11ab +30b^2

Answer 1

А^2 - 5аb-6ab+30b^2 - здесь мы создаём разность 11ab
a(a-5b) - 6b(a-5b) - вынесем общий множитель:
(a-5b)(a-6b)
Удачи!

Answer 2

To factor the expression $a^2 - 11ab + 30b^2$, we can look for two binomials of the form $(a + mb)(c + db)$ that multiply together to give the original expression.

In this case, we need to find $m$, $b$, $c$, and $d$ such that:

$(a + mb)(c + db) = a^2 - 11ab + 30b^2$

To do this, we need to find two numbers that multiply to $30b^2$ (the last term) and add up to $-11ab$ (the middle term).

The two numbers that satisfy these conditions are -5b and -6b because:

$(-5b) \times (-6b) = 30b^2$ (multiplication)

$(-5b) + (-6b) = -11b$ (addition)

Now, we can rewrite the original expression as follows:

$a^2 - 11ab + 30b^2 = a^2 - 5ab - 6ab + 30b^2$

Next, we can group the terms and factor by grouping:

$a^2 - 5ab - 6ab + 30b^2$

$a(a - 5b) - 6b(a - 5b)$

Now, we can factor out the common factor $(a - 5b)$:

$(a - 5b)(a - 6b)$

So, the factored form of the expression $a^2 - 11ab + 30b^2$ is $(a - 5b)(a - 6b)$.