Question

coefficient of z in (z-5)³​

Answer 1

Answer:

75

Step-by-step explanation:

Expand (z - 5)³ using the identity (a - b)³ = a³ - b³ - 3a²b + 3ab²

➥ (z - 5)³

= z³ - (5)³ - (3 × z² × 5) + (3 × z × 5²)

= z³ - 125 - 15z² + (3 × 25z)

= z³ - 125 - 15z² + 75z

= z³ - 15z² + 75z - 125

Coefficient of z in the above expression is 75.

KNOW MORE:

• Coefficient of any algebraic term is the number attached to it excluding the variable.

For example, coefficient of z² here would be -15.

Some useful identities:

• (a + b)³ = a³ + b³ + 3a²b + 3ab²
• (a + b) (a - b) = a² - b²
• (a + b)² = a² + b² + 2ab
• (a - b)² = a² + b² - 2ab
• (a + b + c)² = a² + b² + c² + 2(ab + bc + ac)