Step-by-step please :)
-
x^2-x-a-a^2
= x^2-a^2 - x-a
= (x+a)(x-a) - (x+a)
= (x+a)(x-a-1)
= x^2-a^2 - x-a
= (x+a)(x-a) - (x+a)
= (x+a)(x-a-1)
-
Well, just try to look at it as the familiar situation ax^2 + bx + c ; only that c is more complicated than usual:
x^2-x-a-a^2 ; a = 1; b = -1 and c = -a-a^2
(x )(x ) We need to look for two numbers that added give -1 and multiplied give -a-a^2
Seems tough but notice that -a-a^2 = (a)(-1-a) , so we know that (a) multiplied by (-1-a) gives -a-a^2 but when they are added do we get -1 ? Well, a + (-1-a) = a-1-a = -1 Nice, so:
(x+a)(x-1-a) That's your answer. To confirm, multiply these two factors and you should get back to the original expression.
Hope this helps...
x^2-x-a-a^2 ; a = 1; b = -1 and c = -a-a^2
(x )(x ) We need to look for two numbers that added give -1 and multiplied give -a-a^2
Seems tough but notice that -a-a^2 = (a)(-1-a) , so we know that (a) multiplied by (-1-a) gives -a-a^2 but when they are added do we get -1 ? Well, a + (-1-a) = a-1-a = -1 Nice, so:
(x+a)(x-1-a) That's your answer. To confirm, multiply these two factors and you should get back to the original expression.
Hope this helps...
-
x^2-x-a-a^2=(a-x+1)(a+x)