Homeowkr Help(Polynomials)?

Question

I don't understand mutiply and dividing polynomials.

x^5+x^3= 1^8

Did I get that right.

I need help with this too:

4a^2 * 3a^4

5a^2b^2 * 6ab^5

3m^3(5m^7- 4m)

(-)3x^2(8x^2-2x)

Area of a rectangle

2n * n+4

a^4B^3

-------------

ab2

15a^3 - 10a^2 + 5a

---------------------------

5a

Thank you

Answer 1

x^5 + x^3

You cannot add them. They are not of the same exponent, therefore they are two different types of terms. x^5 + x^3 is as simplified as it gets.

4a^2 * 3a^4 (when you multiply exponents with the same base, you add them, so add the exponents 2 and 4 to get 6)

12a^6 <===

5a^2b^2 * 6ab^5 (again, add the exponents; add 2 and 1 for a, and 2 and 5 for b)

30a^3b^7 <===

3m^3(5m^7 - 4m) (remember the distributive property: x(a + b) = ax + bx; exponent rules still apply)

15m^10 - 12m^4 <===

-3x^2(8x^2 - 2x)

24x^4 + 6x^3 <===

2n(n + 4)

2n^2 + 8n <===

a^4b^3 / ab^2 (when you divide exponents, you subtract the denominator (bottom number or the number you are dividing by) from the numerator (top number or the number being divided))

a^3b <===

(15a^3 - 10a^2 + 5a)/5a

3a^2 - 2a + 1 <===

Answer 2

4a^2 * 3a^4

(4*3) a^2+4

---->12a^6

5a^2b^2 * 6ab^5

(5*6)(a^2+1)(b^2+5)

----->30a^3b^7

3m^3(5m^7-4m)

3m^3 times 5m^7 = 15m^10

3m^3 times -4m = -12m^4

----->15m^10 -12m^4

(-)3x^2(8x^2-2x)

-3x^2(8x^2-2x)

-3x^2 times 8x^2 = -24x^4

-3x^2 times -2x = 6x^3

-----> -24x^4 +6x^3

Area = l * w

2n * n+4

2n times n = 2n^2

2n times 4 = 8n

-----> 2n^2 +8n

a^4b^3

-------------

ab^2

Just minus their exponent...

So...

----->a^3b

15a^3 - 10a^2 + 5a

--------------------------

5a

You need to get the common factor that can be divided by 5a (if any..)

5a (3a^2 - 2a +1)

-------------------------

5a

Now cancel them... the 5a

------>3a^2 - 2a + 1

give me my 10 points... THX