Question

Упростить:(m-2n)^2-3m(m+5n)​

Answer 1

$(m-2n)^2-3m(m+5n)=m^2-4mn+4n^2-3m^2-15mn=\\- 2m^2 - 19mn + 4n^2$

Answer 2

To simplify the given expression, follow these steps:

Step 1: Expand the squared term (m-2n)^2. Step 2: Distribute the -3m into the second term.

Let's start:

Step 1: Expanding (m-2n)^2: (m-2n)^2 = (m-2n)(m-2n) = m(m) - m(2n) - 2n(m) - 2n(-2n) = m^2 - 2mn - 2mn + 4n^2 = m^2 - 4mn + 4n^2

Step 2: Distribute -3m into the second term: -3m(m+5n) = -3m * m - 3m * 5n = -3m^2 - 15mn

Now, combine the results from Step 1 and Step 2:

(m-2n)^2 - 3m(m+5n) = (m^2 - 4mn + 4n^2) - (-3m^2 - 15mn)

Now, when you distribute the negative sign inside the second parentheses, it changes the signs of the terms inside:

= m^2 - 4mn + 4n^2 + 3m^2 + 15mn

Now, combine like terms:

= (m^2 + 3m^2) + (-4mn + 15mn) + 4n^2 = 4m^2 + 11mn + 4n^2

So, the simplified expression is 4m^2 + 11mn + 4n^2.