Question

Someone please help ​

Answer 1

Step-by-step explanation:

polynomial identities means equations where the left and the right side are always identical (no matter what values we use for the variables).

so,

A is not.

(x + 2)³ = x³ + 8

(x+2)(x+2)(x+2) = x³ + 8

(x² + 4x + 4)(x+2) = x³ + 8

x³ + 4x² + 4x + 2x² + 8x + 8 = x³ + 8

x³ + 6x² + 10x + 8 is definitely not generally the same as x³ + 8

B is not.

x⁶ + x = (x-1)(x⁵ + x⁴ + x³ + x² + x)

x⁶ + x = x⁶ + x⁵ + x⁴ + x³ + x² - x⁵ - x⁴ - x³ - x² - x

x⁶ + x = x⁶ - x

that is definitely not generally equal.

C is an identity

(x² - 1)(x⁴ + x² + 1) = x⁶ - 1

x⁶ + x⁴ + x² - x⁴ - x² - 1 = x⁶ - 1

x⁶ - 1 = x⁶ - 1

yes, identical.

D is not.

(x+1)⁴ = x⁴ + x³ + x² + x + 1

(x+1)²(x+1)² = x⁴ + x³ + x² + x + 1

(x²+2x+1)² = x⁴ + x³ + x² + x + 1

x⁴ + 2x³ + x² + 2x³ + 4x² + 2x + x² + 2x + 1 =

x⁴ + 4x³ + 6x² + 4x + 1

that is definitely not generally the same as

x⁴ + x³ + x² + x + 1

E is an identity

(x+1)(x⁴ - x³ + x² - x + 1) = x⁵ + 1

x⁵ - x⁴ + x³ - x² + x + x⁴ - x³ + x² - x + 1 =

x⁵ + 1 = x⁵ + 1

yes, identical.

F is an identity

(x³-1)(x³+1) = x⁶ - 1

x⁶ + x³ - x³ - 1 = x⁶ - 1

x⁶ - 1 = x⁶ - 1

yes, identical.