A few questions please help

[Joebird]

I need help with some of these questions:

1) How many terms will there be in your answer when you multiply and simplify (x + y)^3
I know it's written like (x + y)(x + y)(x + y) Which would be x^3 + y^3 But I when I gave the answer of 3 terms, I got it wrong. Not sure how many terms?

2) When 4x - x^2 - 4y + xy is factored completely, one of the factors is?
Would one of the factors be (2x + y) ?

3) Solve by factoring: 3x^2 - 8x + 5 = 0
Not sure how to solve this one, could anyone please explain?

4) What direction does the parabola y = -2(x + 3)^2 - 5 open?
I'm trying to solve this one right now.


Thanks for any help!

 

[tkhunny]

I need help with some of these questions:

1) How many terms will there be in your answer when you multiply and simplify (x + y)^3
I know it's written like (x + y)(x + y)(x + y) Which would be x^3 + y^3 But I when I gave the answer of 3 terms, I got it wrong. Not sure how many terms?

"Terms" generally, are things separated by addition or subtraction.

x^3 + y^3 has TWO terms

However, (x + y)(x + y)(x + y) most certainly is NOT x^3 + y^3

Let's do a test case.

11^3 = 11*11*11 = 1331
11 = 10+1
(10+1)*(10+1)*(10+1) = 10^3 + 1^3 = 1000 + 1 = 1001 <== Whoops! That can't be right.
Do you know that you can think up useful experiments to disprove various things? It is a very useful tactic.

Back to the problem.
[(x + y)(x + y)](x + y) = (x^2 + 2xy + y^2)*(x+y) = x^3 + 3(x^2)y + 3xy^2 + y^3

That differs substantially from your result. Remember how to multiply. Don't look for a trick or a shortcut.