Question

Zero product property to solve equations

1. a^2+8a=0
2. (3h-6)(2h-8)=0
3. 6m^2+17m+5=0
4. y^2-36=0
5. (3g+4)^2=0

Answer 1

1. a² + 8a = 0
a(a) + (8) = 0
a(a + 8) = 0
a = 0 or a + 8 = 0
- 8 - 8
a = -8

2. (3h - 6)(2h - 8) = 0
(3(h) - 3(2))(2(h) - 2(4)) = 0
(3(h - 2))(2(h - 4)) = 0
6(h - 2)(h - 4) = 0
6 6
(h - 2)(h - 4) = 0
h - 2 = 0 or h - 4 = 0
+ 2 + 2 + 4 + 4
h = 2 h = 4

3. 6m² + 17m + 5 = 0
6m² + 15m + 2m + 5 = 0
3m(2m) + 3m(5) + 1(2m) + 1(5) = 0
3m(2m + 5) + 1(2m + 5) = 0
(3m + 1)(2m + 5) = 0
3m + 1 = 0 or 2m + 5 = 0
- 1 - 1 - 5 - 5
3m = -1 2m = -5
3 3 3 3
m = ⁻¹/₃ m = -1²/₃

4. y² - 36 = 0
y² - 6y + 6y - 36 = 0
y(y) - y(6) + 6(y) - 6(6) = 0
y(y - 6) + 6(y - 6) = 0
(y + 6)(y - 6) = 0
y + 6 = 0 or y - 6 = 0
- 6 - 6 + 6 + 6
y = -6 y = 6

5. (3g + 4)² = 0
(√(3g + 4))² = √(0)
3g + 4 = 0
- 4 - 4
3g = -4
3 3
g = -1¹/₃