algebra help plz...multiplying polynomials...?

Question

For questions 1- 5, multiply the following polynomials.

1. (x-3) (x+3)

2. (2a+5b) (3a-7b)

3. (3x+8)squared

4. (x squared -3x+5) (2x squared +5x-3)

5. (2a-3b) (4a squared +5ab-7b squared)

For questions 6-10, find the GCF and factor the following polynomials.

6. 3x cubed -6x squared +3x

7. -24m raised 6 +12m raised 4 -48m raised 5

8. 5p raised 3 t raised 2+25p raised 2 t raised 3-30pt raised 4

9. 3m raised 6 n raised 4 p raised 5+6m raised 4 n raised 5 p raised 3 -9m raised 3 n raised 5 p raised 6

10. 12(2z+1) cubed+10(2z+1) squared-25(2z+1)

Answer 1

1) (x^2) - 9
2) (6a^2) - (35b^2) + 1ab
3) (9x^2) + 48x + 64
4) (2x^4) -(x^3) - (8x^2) + 34x -15
5) that's all for now...

Answer 2

Not going to do all 10 of them for you. But I will walk you through a couple.

1) (x-3)(x+3)

remember FILO...First, inner, outer, last.

FIRST: multiply the first terms of the polynomials:

x * x = x^2

INNER: multiply the two inner terms

-3 * x = -3x

OUTER: multiply the two outer terms

x * 3 = 3x

LAST: multiply the two last terms

-3 * 3 = -9

Now add all of these together and simplify.

x^2 - 3x + 3x -9

= x^2 - 9

questions 2 through five are done the same way. For those with 3 terms, you need to multiply all three of the terms with all of the terms in the other polynomial.

6. 3x^3-6x^2+3x

First part - what's the GCF? This is the greatest factor which can evenly divide into all three terms of the polynomial. A little trial and error will show that this is 3x.

Part 2 is to completely factor the polynomial. Well, you know 3x is a factor (it's the GCF). So pull it out and simplify

(3x)(x^2-2x+1)

now we have to factor the polynomial x^2-2x+1

(x-1)(x-1) = x^2-2x+1
(to prove it, multiply as in problem 1)

So the polynomial factorization is (3x)(x-1)(x-1)

Questions 7 through 10 are done the same way. First figure out the GCF, then pull it out and factor the rest.

Answer 3

Questions 1-5 all require that you use the distribution rule.
For example, the first one is

( x - 3 ) ( x + 3 )
x ( x + 3 ) - 3 ( x + 3)
x^2 + 3x - 3x + 3^2
x^2 + 9

To solve the last five, you must factor out common terms. For example, your number 6 is

3x^3 - 6x^2 + 3x

Each term can be divided by 3x, so do so

( 3x ) ( x^2 - 2x + 1 )

The second term can be factored, so you finally get

( 3x ) ( x - 1 ) ( x - 1 )
( 3x ) ( x - 1 )^2

The others are solved in a similar fashion.

Answer 4

1. x (squared) - nine
2. 6c (squared) + 8ab - 35b (squared)
3. 9x (squared) + 48x + 64
4. 4x (to the fourth) - x (cubed) - 8x (squared) + 25x - 6
5. 8a (cubed) - 2a(squared)b - 24ab(squared) +21b(cubed)

and then I got bored. sorry. maybe more help later.