Binomial theorem Expand (5 - y)3

Mathematics

1 answer:

Snowcat [4.5K]3 years ago

7 0

Answer:

(5 - y) ^3 = 125 - 75y + 15y^2 - y^3

Step-by-step explanation:

Binomial expression

1. 1

1. 2. 1

1. 3. 3. 1 --------power of 3

( 5 - y) ^3

( 5 - y) (5 - y) (5 - y)

( a + b) ^3 = a^3 + 3a^2b + 3ab^2 + b^3

a = 5

b = -y

( 5 - y) ^2 = ( 5 - y) (5 - y)

= 5( 5 - y) - y(5 - y)

= 25 - 5y - 5y + y^2

=(25-10y+y^2)

( 25 - 10y + y^2)( 5 - y)

= 5(25 - 10y + y^2) - y( 25 - 10y + y^2)

= 125 - 50y + 5y^2 - 25y + 10y^2 - y^3

Collect the like terms

= 125 - 50y - 25y + 5y^2 + 10y^2 - y^3

= 125 - 75y + 15y^2 - y^3

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