To solve factors of 2a2 + a - 15, use these steps:
1) What are the factors of 2a2? The choices are 2a2 x 1 and 2a x a
2) What are the factors of 15? The choices are 1x15 and 3x5.
We can setup the factors to look like this:
(A ± B) * (C ± D)
Because the last term in the expression is negatie (-15), the signs must be opposite. Therefore:
(A + B) * (C - D)
Since the middle term is positive, the product of B*C (which is positive) must be greater than the product of A*D (which is negative).
At this point, you simply need to guess and check the possibilities. Substitute 2a and a (from step 1) for A and C, and 3 and 5 (from step 2) for B and D to yield:
(2a - 5) * (a + 3)
Therefore, the factos of 2a2 + a - 15 are (2a - 5) and (a + 3)
That factors to (2a - 7)(2a + 9)
a + a + a - 2a = 3a - 2a = a
4a2+ 25 does not factor over the real number field. In the complex numbers , it factors as (2a +5i)(2a - 5i). This is because i2 = -1, so 4a2 + 25 = 4a2 - (- 25) = 4a2 - 25(-1) = 4a2 - 25i2
2a + a = 3a
9a +8 -2a -3 -5a = 2a +5
4a
What is the solution of -2a plus 3a plus 5b
2a + 3a = 5a
8b -2a
n2 - 4 is the "difference of two squares." That factors to (n - 2)(n+2)a2 + 2a + 1 is "additive squares." That factors to (a + 1)(a + 1) or (a + 1)2
x + 2a
(6ab + 9b)/(2a + 3) = 3b(2a + 3)/(2a + 3) = 3b