When the coefficient of x^2 is more than 1, then factoring occurs this way:
-You list the factors of the coefficient of x^2
- || || || || || || constant.
-You must find a method so that (the first factor of one of the factors of x^2 * the last factor of one of the factors of x) + (the second one of that same factor of x^2 * the first one of that same factor of x) = the coefficient of x. If this condition is met, then those are the numbers which you put in the factoring. An example is equal to an infinite sequence of words:
Factors of 4: (4)(1),(1)(4),(-4)(-1),(-1)(-4),(2)(2),(-2)(-2)
Factors of 9: (3)(3),(-3)(-3),(9)(1),(-9)(-1)
Let's try... say (1)(4) and (9)(1)
1*1=1
4*9=36
1+36 = 37 NOT (-12)
Now, (-2)(-2) and (3)(3)
(-2)(3)=(-6)
(-2)(3)=(-6)
(-6)+(-6) = (-12) YES, that's a (-12)!
y=(-2u+3)(-2u+3)=(-2u+3)^2
That could look baffling now, but over time, you could solve that kind of factoring problems in your head actually.. errrr, you might need to organize the factors in a table of some sort, however.
If you are familiar with foiling it is the best method. Start with two sets of blank paranthesis. The first variable usually doesn't have a constant or number but in this case there is. What times what will give you 4u squared? 2u times 2u. then what times what equals 9? in this case there is only one choice. 3 times 3. then to decide the signs in each of the paranthesis depends on the middle variable. since it is negative 12 each will negative because 2u times -3 equals -6 and -6 plus -6 gives you -12.
Comments
( 2u - 3 ) ( 2u - 3 ) = ( 2u - 3 ) ²
When the coefficient of x^2 is more than 1, then factoring occurs this way:
-You list the factors of the coefficient of x^2
- || || || || || || constant.
-You must find a method so that (the first factor of one of the factors of x^2 * the last factor of one of the factors of x) + (the second one of that same factor of x^2 * the first one of that same factor of x) = the coefficient of x. If this condition is met, then those are the numbers which you put in the factoring. An example is equal to an infinite sequence of words:
Factors of 4: (4)(1),(1)(4),(-4)(-1),(-1)(-4),(2)(2),(-2)(-2)
Factors of 9: (3)(3),(-3)(-3),(9)(1),(-9)(-1)
Let's try... say (1)(4) and (9)(1)
1*1=1
4*9=36
1+36 = 37 NOT (-12)
Now, (-2)(-2) and (3)(3)
(-2)(3)=(-6)
(-2)(3)=(-6)
(-6)+(-6) = (-12) YES, that's a (-12)!
y=(-2u+3)(-2u+3)=(-2u+3)^2
That could look baffling now, but over time, you could solve that kind of factoring problems in your head actually.. errrr, you might need to organize the factors in a table of some sort, however.
-Zzzzzzzzzzzzzzzzz... Aw! Oh, Answer Detective.
(2u-3)(2u-3)
If you are familiar with foiling it is the best method. Start with two sets of blank paranthesis. The first variable usually doesn't have a constant or number but in this case there is. What times what will give you 4u squared? 2u times 2u. then what times what equals 9? in this case there is only one choice. 3 times 3. then to decide the signs in each of the paranthesis depends on the middle variable. since it is negative 12 each will negative because 2u times -3 equals -6 and -6 plus -6 gives you -12.
Use the master product:
4*9 =36 then find factors of 36 that add up to -12
-6*-6
now replace the -12u with -6u and -6u so
4u^-6u-6u+9 now group them into groups of 2
4u^2-6u and -6u+9
2u(2u-3) + 3(2u-3)
bring the (2u-3) to the front and then put whats left besides it (2u+3)
so final answer is
(2u-3)(2u+3)
This is the square of the difference of two squares.
We have (2u^2)-12u+3^2
Now, (a-b)^2=a^2-2ab+b^2
Here this is (2u-3)^2
(2u-3)(2u-3) or (2u-3)^2
2u x 2u = 4u^2
-6u-6u= -12u
-3 x -3 = +9
Do you know how to FOIL? if so, use that.