Question

10. Using formula, solve:
a) 16c⁴-81d⁴
b) 78 X 82​

Answer 1

Step-by-step explanation:

1. 16c^4-81^4d
2. {(2c)^2}^2-{(3d)^2}^2
3. (2c^2_3d^2)(2c^2+3d^2)
4. (2c-3d)(2c+3f)(4c^2+9d^2)

b)

78×82

(80-2)×(80+2)

6400-4

6396

Answer 2

Answer:

a) [(2c - 3d) (2c + 3d)] [4c² + 9d²]

b) 6,396

Step-by-step explanation:

a) 16c⁴ - 81d⁴

= [(2c)²]² - [(3d)²]²

Using identity,

(a² - b²) = (a - b) (a + b)

a = (2c)²

b = (3d)²

= [(2c)² - (3d)²] [(2c)² + (3d)²]

Using identity,

(a² - b²) = (a - b) (a + b)

= [(2c - 3d) (2c + 3d)] [4c² + 9d²]

b) 78 × 82

= (80 - 2) × (80 + 2)

Using identity

(a² - b²) = (a - b) (a + b)

= (80² - 2²)

= (6,400 - 4)

= 6,396