[bemiz0112]

Find and simplify let P(x)=X^2x+3
1.p(-y)

Simplify
2.(2b^2+3b-5)-(2b^2-4b-9)

simplify
3. 3y(y+2)+(y+1)(y-1)

simplify write all results with positive exponents

4. -5(a^2b)^3 ____=divide
___________
10(ab)^3

Factor

5. 2x^2+2xy-3x-3y

[jcaron2]

Find and simplify let P(x)=X^2x+3
1.p(-y)

Well, you have P(x); you're supposed to find P(-y). So just take the equation for P(x), and everywhere you see an x, replace it with a -y. So what do you get?

Simplify
2.(2b^2+3b-5)-(2b^2-4b-9)

There are two things to keep in mind here:

1) Remember that whenever you subtract something in parentheses, you need to distribute the minus sign throughout. For example, -(5x^2 + 6x -3) = -5x^2 -6x +3.

2) You can add or subtract like terms to simplify. For example, 3x^2 + 2x^2 = 5x^2. Or 2x - 6x = -4x. But you can't combine unlike terms. For example, 3x^2 - 2x can't be simplified any more than it already is.

So just get rid of the parentheses by distributing the minus sign like in advice #1, then combine all the like terms like in advice #2.

simplify
3. 3y(y+2)+(y+1)(y-1)

You just need to multiply out the two products, 3y*(y+2) and (y+1)(y-1) to get everything in terms of y^2 and y. Then combine like terms.

simplify write all results with positive exponents

4. -5(a^2b)^3 ____=divide
___________
10(ab)^3

First, you'll want to distribute any exponents after parentheses:



Then go through and cancel common factors in the numerator and denominator. For example, the -5 in the numerator and the 10 in the denominator reduce to a -1 and a 2 respectively (since you can cancel out the common factor of 5). Likewise, whenever there's a variable in both the numerator and the denominator, subtract the exponents and put the variable to the resulting power in the numerator. If the exponent turns out to be negative, put the variable in the denominator instead and then make the exponent positive. Also, remember that if the resulting exponent is 0, the variable cancels out entirely (since anything to the 0 power is equal to 1). And finally, remember that a variable with no exponent written means that it's raised to the 1 power. In other words, its exponent is 1. Here's an example that's similar to your problem, but a little different:

Factor

5. 2x^2+2xy-3x-3y

You're mostly going to have to use some intelligent trial-and-error here, the same way you'd factor anything else. I'll give you a hint. It will look like this:

(?x+?y)(?x-?)

You just need to figure out what numbers go in place of the question marks.