how do i factor 8m^2-6mn-9n^2
If you had
8x^2 - 6x - 9 can you see how I factored it to
(4x+3)(2x-3) ?
8x^2 - 6x - 9
For this problem we have to multiply the first and the last term here the first term is 8 and the last term is -9 if we multiplied this two we will get -72 then we have to split this number in to two parts and the multiplication value of splitted term must be equal to -72 and the simplification value must be equal to the midlle term that is -6 .So we can split 72 as (-12)*6
8x^2-6x-9 = (2x-3)(4x+3)
To factor the expression 8m^2 - 6mn - 9n^2, follow these steps:
Step 1: Look for a common factor, if any. In this case, there is no common factor among the terms.
Step 2: Check if the expression is a perfect square trinomial or a difference of squares. In this case, it is neither a perfect square trinomial nor a difference of squares.
Step 3: Factor the expression using the tried-and-true method for trinomials, which is using the FOIL (First, Outer, Inner, Last) method. Here's how it works:
- Write down two sets of parentheses.
- In the first position of each set, write down the factors of the first term (8m^2), which are 2m and 4m.
- In the last position of each set, write down the factors of the last term (-9n^2), which are -n and 9n.
- To find the middle term (-6mn), you need to determine which combination of the factors in the first and last positions can be multiplied to get this term, considering the signs. In this case, -3n and 2m should be used, like this:
(2m - 3n)(4m + 3n)
So, the factored form of the expression 8m^2 - 6mn - 9n^2 is (2m - 3n)(4m + 3n).