Can Someone help me simplify these math problems?

Question

1. 8z^2 + cz + 35 = (4z + 7) (2z+5)
what is the value of c

2. (a^2 + 6a + 9) / (a^2 - 9)

3. (1/x) + (1/y)

4. length 2x^2+10
width x^2+2x+2
find the perimeter

Answer 1

1. Multiply it out by FOIL, then cancel out like terms
8z^2 + cz + 35 = (4z + 7) (2z+5)
8z^2 + cz + 35 = 8z^2 + 34z + 35
cz = 34z
c = 34

2. Factor, then cancel out a common factor in both the numerator and denominator.

(a^2 + 6a + 9) / (a^2 - 9)
(a + 3)(a + 3) / (a - 3)(a + 3)
(a + 3)/(a - 3)

3. Place in common denominator
(1/x) + (1/y)
(y/xy) + (x/xy)
(x+y)/xy

4. Assuming a rectangle
p = 2L + 2W
p = 2(2x^2+10) + 2 (x^2+2x+2)
p = 4x^2 + 20 + 2x^2 + 4x + 4
p = 6x^2 + 4x + 24