That doesn't factor neatly. Applying the quadratic formula, we find two real solutions:
24 plus or minus 6 times the square root of 14
a = 46.44994432064365
a = 1.5500556793563511
a^(3) + a^(2) Factors to a^(2) [ a^(2) + 1 ] NB THe terms in the square brackets do NOT factor. Reason, Any ywo squared terms with a positive (+) between then does NOT factor Think of a^(2) + 1 as a^(2) + 1^(2) . A pair of squared terms with a negative between them DOES factor. So if you initial expression was a^(4) - a^(2) Then a^(2) [ a^(2) - 1^(2)] a^(2)[a - 1)(a + 1) Fully factored. Note the two different signs.
a2 - 4a + 4
a2+9a+20 = (a+4)(a+5) when factored
(a2+2b2-2ab)(a2+2b2+2ab)
It is: (a+1)(a+3) when factored
(a + 9)(a - 3)
a2 + 12a + 27 = (a + 3)(a + 9)
(a+b+c) (a+b-c)
a2(2a2-21a+49) a2(2a-7)(a-7)
a2 - a - 72 = (a - 9)(a + 8)
a2 + 28a + 27 = 0 (a + 1)(a + 27) = 0 a = -1 or -27 However, the second line is the factorised form, the third is what a is equal to
(a2 + 2a + 1)/(5a + 5)factor, top and bottom(a + 1)(a + 1)/5(a + 1)cancel an (a + 1) top and bottom= (a + 1)/5=========