Math question (algebra factorization)?

Question

correct answer
m^2 - 3 + m - 7m + 12
m^2 - 6m + 9
m^2 - 3m - 3m +9
m(m - 3) - 3(m - 3)
(m - 3) (m - 3)
(m - 3)^2

why not
m^2 - 3 + m - 7m + 12
m^2 + 9 - 6m
m^2 + 9 - 3m - 3m
m^2 - 3m + 9 - 3m
m(m - 3) + 3(3 - m)
(m + 3) (m-3)
m^2 3^2

what was the mistake for the 2nd working?

Answer 1

In the second to last line of the second working, you changed (3-m) to (m-3), which introduced a factor of -1 to that term. Thus, you should have also multiplied the coefficient of (3-m), in this case +3, by a factor of -1, changing it to -3.

Answer 2

Your problem begins in the third to the last line:

m^2 - 3 + m - 7m + 12
m^2 + 9 - 6m
m^2 + 9 - 3m - 3m
m^2 - 3m + 9 - 3m
m(m - 3) + 3(3 - m)<~~~~~~~here
(m + 3) (m-3) <~~~~~~~~~~and here
m^2 3^2

First, (m-3) does NOT equal (3-m)
Second, (m+3)(m-3) can NOT be further reduce.

Your solution should read like this, beginning at the fourth line of your work . . .
m^2 - 3m + 9 - 3m
m(m-3)+3(-1)(-3+m) or m(m-3) - 3(m-3) {these are the same}
Therefore,
(m-3)(m-3)
(m-3)^2

Answer 3

I think the mistake begins in the line:

m(m - 3) + 3(3 - m)

We need to realize that: m(m - 3) + 3(3 - m) is NOT the same as m(3 - m) + 3(3 - m).

In truth:
m^2 - 3 + m - 7m +12
= ...
= m(m - 3) + 3(3 - m)
= m (-1)(-m + 3) + 3(3 - m)
= -m(3 - m) + 3(3 - m)
= (-m + 3) (3 - m)
= (3 - m) (3 - m)
= (3 - m)^2
= [(-1)(-3 + m)]^2
= [(-1)^2](m - 3)^2
= (1)(m - 3)^2
= (m - 3)^2
= correct answer

I hope this helps! Good luck =)

Answer 4

the mistake is after the step m(m-3)+3(3-m). note that the term in the bracket are not the same. m-3 and 3-m. the second term should be -3(-3+m) which is the same as -3(m-3). To complete
m^2-3m+9-3m
m(m-3)-3(-3+m)
m(m-3)-3(m-3)
(m-3)(m-3)
(m-3)^2

Answer 5

You are factoring a trinomial (three terms) in your question. The trinomial in question contains two perfect squares: m^2 and 9. This means The factors that make it up are two binomials (a binomial is two terms). The square root of m^2 is m and the square root of 9 is 3. To determine whether the two binomials will each be the sum of two single terms or monomials (the square roots), the difference between these same monomials or one will be a sum and the other will be a difference, we look at the middle term of the original trinomial and the possible sum/difference combinations of the second monomials or square root, in this case 3 and 3. The combination of the monomials that results in the coefficient of the second term (number in front of the variable) will give you your answer: (3) + (3) = (6), (-3) + (-3) = (-6). Thus the answer is (m - 3)(m - 3).

Answer 6

beacuse from the bottom answer (m+ 3)(m-3)= m^2-3m+3m-9 which does not equal m^2-6m+9 from above.
The first answer is correct.

Answer 7

m^2 - 3 + m - 7m + 12
m^2 + (1 - 7)m + (-3 + 12)
m^2 - 6m + 9
(m - 3)^2

--------------------------------

Here is the mistake

m(m - 3) + 3(3 - m)
m(m - 3) + 3(-m + 3)
m(m - 3) + 3(-1(m - 3))
m(m - 3) - 3(m - 3)
(m - 3)(m - 3)

so basically
the factor (m - 3) isn't the same as the factor (3 - m)

to be able to combine them, they have to look exactly the same.

Answer 8

Factoring

m² - 3 + m - 7m + 12

m² -6m + 9

Collecting like terms

m² - 6m + 9 = (m - 3)(m - 3)

The factoring is complete

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

Proof

(m - 3) (m - 3) = m² - 3m - 3m + 9 = m² - 6m + 9

The FOIL Method

Answer 9

The error is from line 5 to line 6.

m(m-3)+3(3-m) is not equal to

(m+3)(m-3)

You have to change signs
m(m-3)+3(3-m) = m(m-3)-3(m-3)
(m-3)(m-3)
(m-3)^2

Answer 10

m(m - 3) + 3(3 - m)
(m + 3) (m-3)
m^2 3^2

mmmmmm....
(3 - m) is not the same as (m - 3)

THAT'S WHY NOT.