These problems really trip me up. I usually extend out to the problem, but then I’m unsure on how to group them. Please help? Thank You so much!
If a2+xa+18=(a+y)(a+3) for all values of a and for constants x and y, what is x?
Well, we have:
a^2 + xa + 18 = (a + y) (a + 3)
Let’s FOIL the right side so we have both sides in the same format
a^2 + xa + 18 = a^2 + ya + 3a + 3y
The 2nd and 3rd terms of the right hand side can be combined
So we get
a^2 + xa + 18 = a^2 + (3+y)a + 3y
We can cancel a^2 on both sides.
xa + 18 = (3+y)a + 3y
On the left hand side, we have xa + 18. a is a variable, 18 is a constant.
On the right hand side (3+y)a is a variable, 3y is a constant (it says in the problem y is a constant, so 3 x constant will just be a number aka constant)
Set the variable like terms equal to each other:
xa= (3+y)a, we can cancel both a so we just get x= 3 + y
Set the constants equal to each other:
18 = 3y
LOOK! we can solve for 18=3y with simple algebra, giving us y=6.
If we plug y=6 into x = 3+y, we get x=9.
That’s your answer: x=9.