Help a struggling mom

Hi, I have been working with my son all day on 60 algebra problems and there's several we can't get. Please help.

1. Write an expression for the product of two and the sum of four and twice a number.

2. simplify 35-7(3z-2)
(our answer): -21z+49

3. Perform the indicated operations:
(7x^3-5x+2)-(5x^3-4x^2+6x-7)

4. Simplify (3x^2)(-2x^5)
(our answer): -6x^7

5. Simplify (5ab^3)^2
(our answer): 25a^3b^5

6. Simplify (4a^3)^2(3a)^2
(our answer): 144a^8

7. Simplify 10x^5y^4/15x^3y^9

8. Factor completely: x^2+4x-16

9. Solve the equation (x+6)(x-7)(x-8)(x+9)=0

10. Find the dimensions of the rectangle if the width is 3 feet less than the length and the area is 40ft^2.

11. Simplify: (6x/5y)(10y/8x)

Thank you in advance for any help you can give

2. simplify 35-7(3z-2)

=35 - 21z+14 (the key step to watch out for is to make sure you multiply both the items inside the brackets by -7, not just 7.
=35 + 14 - 21z
=49-21z

3. Perform the indicated operations:
(7x^3-5x+2)-(5x^3-4x^2+6x-7)
with this one rewrite the problem by using the minus sign on each on the elements inside the second set of brackets, like this

6x-(4x-5x^2+3)
=6x -4x+5x^2 - 3

4.Simplify (3x^2)(-2x^5)

with power problems you muliply the bottom numbers together (3x2)=6
and with the powers of "x" you add the powers (x^2)(x^3)=x^5

5. Simplify (5ab^3)^2
Powers raised to powers are muliplied (x^3)^2 = x^6

(5a b^3)^2= (5a b^3) x (5a b^3)

=(5x5) (axa) (b^3 x b^3)

=25a^2 b^6

7. the use of a divide is treated as a minus sign when applied to powers ie

a^7/ a^5 = a^(7-5) =a^2

Have a go at solving these now and post your efforts after using the above as a guide.

Still stuck on #3

ok, i got as far as: 2x^3+4x^2-11x+9 but I don't know how to factor down further.

Please check answer to #7

the answer we came up with for #7 is:
2x^2/3y^5

10x^5y^4/15x^3y^9
=((10x^5)(y^4)/(15x^3)(y^9))
=(10/15)(x^(5-3)) / (y^(4-9)) .

=(10/15) (x^2)/(y^-5)

=(2/3) (x^2) (y^5)

so I differ in the y^5 ---it is a postive when you drop the divide sign.

3.Perform the indicated operations:
(7x^3-5x+2)-(5x^3-4x^2+6x-7)


and your answer is correct
2x^3+4x^2-11x+9

1. Write an expression for the product of two and the sum of four and twice a number.

Not very clear; I think what is meant is:
product of "2" and "4 + twice a number"

let n = "a number"; so expression is:
2 times (4 + 2 times n) or 2(4 + 2n)

NOTE: not sure what's preferred, 11 problems in one post
or 11 posts of 1 problem each...I prefer 11 posts...moderators??