how do you solve (3m-n)(2m-5n)?

Answer 1

There's nothing to SOLVE, except:

WHAT IS YOUR PROBLEM ?!

A.) I suspect that you mean (3m-n)(2m-5n) = 0, that is an EQUATION.

(You only wrote an EXPRESSION; without setting that equal to SOMETHING --- and it needn't necessarily be zero --- there's NOTHING to SOLVE.)

O.K, so IF the problem is

(3m-n)(2m-5n) = 0,

then m = either n/3 or 5n/2,

because if the product of two different quantities is zero, then one of those quantities must itself be zero.

Since it isn't clear whether m or n is the independent variable, you can also express the solutions as

n = 3m or 2m/5.

B.) If, on the other hand you meant "How do you expand/distribute this expression?", please understand that if this is what you REALLYmeant, you're NOT "solving" anything at all --- you're simply RE-EXPRESSING the original expression. That is certainly a valid mathematical thing to do, but we don't call it "solving" the expression. That's simply the wrong language to use in this context.]

To distribute the quantities in two two-term parentheses like this, use the mnemonic FOIL (for First, Outer, Inner, Last) --- referring to the successive pairings of the four terms in the original expression.

Using that approach, one finds

(3m-n)(2m-5n) = 6 m^2 (F) - 15 mn (O) - 2 mn (I) + 5 n^2 (L)

= 6 m^2 - 17 mn + 5 n^2.

This is the "baby steps" way of expanding/distributing such expressions. However, with enough practice you should move beyond that. Notice that the result must necessarily involve only terms in m^2, mn and n^2. So, mentally, you just pick up the necessary paired terms that will give you that. (It will also work with expressions like (ax + b)(cx + d) --- there'll be terms in x^2, x [that is, x^1] and just the constant [that is, x^0] terms, then.)

See if you can understand why that process applied to your problem must necessarily produce

6 m^2 - (15 + 2) mn + 5 n^2 = 6 m^2 - 17 mn + 5 n^2.

This "pattern recognition" method might not seem much simpler, but with practice it becomes second nature to write down such "obviously paired" combinations mentally without spending time worrying about "WHICH terms ARE those corresponding to the letters F, O, I, and L?!"


Live long and prosper.

Answer 2

it can not be solve because there are two unknow variables. Perhaps, you meant to expand.

(3m - n) (2m - 5n)

distribute
6m^2 - 15mn - 2mn + 5n^2

combine like terms
6m^2 - 17mn + 5n^2

Answer 3

You need to specify whether you are solving for m in terms of n, or n in terms of m. You also need to equate this expression to a known value t:

Expand the product:
6m^2 - 17mn + 5n^2 = t

If it's m you want to find, treat this as a quadratic equation:
6m^2 - (17n)m + (5n^2 - t) = 0
and use the quadratic formula.
If it's n, treat it as:
5n^2 - (17m)n + (6m^2 - t) = 0.

Answer 4

There are no = signs therefore no equation and no solution.
However, the brackets may be multiplied:-
(3m - n).(2m - 5n)
= 6m² - 17mn + 5n²

Answer 5

you use foil (First Outer Inner Last)

so you get 3m *2m then 3m *5n then -n*2m and finally -n *-5n so you get

6m^2-15mn-2mn-5n^2
which simplifies to


6m^2-17mn-5n^2

Answer 6

(3m-n)(2m-5n)
6m^2 -15mn -2mn + 5n^2
6m^2 -17mn + 5n^2