Question

I really need help , im so confused .I need someone to go over it with me .

Prove the polynomial identity.

(a−1)^3+(a−1)^2=a(a−1)^2

Drag and drop the expressions to correctly complete the proof of the polynomial identity.

The options and blank spaces they give me are in the attachements

Answer 1

We use these identities:

`(a-b)^(3) = a^(3) - 3a^(2)b + 3ab^(2) - b^(3)` and

`(a-b)^(2) = a^(2) - 2ab + b^(2)`

Please follow the below steps to fill the answers:

`(a - 1)^(3) + (a - 1)^(2) = a(a - 1)^(2)`

`a^(3) - 3a^(2) +3a - 1 + a^(2) - 2a + 1 = a(a - 1)^(2)`

`a^(3) - 2a^(2) +a = a(a - 1)^(2)`

`a(a^(2) - 2a + 1 ) = a(a - 1)^(2)`

`a(a - 1)(a - 1) = a(a - 1)^(2)`

`a(a - 1)^(2) = a(a - 1)^(2)`