Question

Помогите разложить на множители: 1) m^2-7mn+12n^2 ; 2) a^2-7ab+10b^2 пожалуйста, нужно очень.

Answer 1

1) m^2 - 4mn - 3mn + 12n^2 = m(m - 4n) - 3n(m - 4n) = (m - 4n)(m - 3n) 
2) a^2 - 5ab - 2ab + 10b^2 = a(a - 5b) - 2b(a - 5b) = (a - 5b)(a - 2b)

Answer 2

Factoring Expressions:

To factor the given expressions, we need to find two binomials whose product is equal to the given expression. Let's factor each expression one by one.

1) m^2 - 7mn + 12n^2:

To factor this expression, we need to find two binomials whose product is equal to the given expression. We can do this by looking for two numbers that multiply to give the constant term (12n^2) and add up to give the coefficient of the middle term (-7mn).

The constant term is 12n^2, which can be factored as 4n^2 * 3n^2 or 2n * 6n^2. Now, we need to find two numbers that add up to -7mn. The numbers that satisfy this condition are -4n and -3n.

Therefore, we can factor the expression as:

m^2 - 7mn + 12n^2 = (m - 4n)(m - 3n)

2) a^2 - 7ab + 10b^2:

To factor this expression, we need to find two binomials whose product is equal to the given expression. We can do this by looking for two numbers that multiply to give the constant term (10b^2) and add up to give the coefficient of the middle term (-7ab).

The constant term is 10b^2, which can be factored as 2b^2 * 5b^2 or 1b * 10b^2. Now, we need to find two numbers that add up to -7ab. The numbers that satisfy this condition are -2b and -5b.

Therefore, we can factor the expression as:

a^2 - 7ab + 10b^2 = (a - 2b)(a - 5b)

So, the factored forms of the given expressions are:

1) m^2 - 7mn + 12n^2 = (m - 4n)(m - 3n) 2) a^2 - 7ab + 10b^2 = (a - 2b)(a - 5b)

I hope this helps! Let me know if you have any further questions.