Question

Cool Down: A Cubic Identification Is (a + b)(a'- ab + b?) =a +b an identity? Explain or show your reasoning.

Answer 1

The given expression is not an identity because expression
`\( aa' + ba' + ab' - a^2b - ab^2 + bb' \)` is not equal to a + b.

How to show proof?

The expression
`\((a + b)(a' - ab + b')\)` is not an identity equal to a + b.

To demonstrate this, let's perform the multiplication and simplify:

`\[ (a + b)(a' - ab + b') = a(a' - ab + b') + b(a' - ab + b') \]`

Now distribute and simplify:

`\[ a \cdot a' - a \cdot ab + a \cdot b' + b \cdot a' - b \cdot ab + b \cdot b' \]`

Combine like terms:

`\[ aa' - a^2b + ab' + ba' - ab^2 + bb' \]`

Now, reorder the terms:

`\[ aa' + ba' + ab' - a^2b - ab^2 + bb' \]`

The expression
`\( aa' + ba' + ab' - a^2b - ab^2 + bb' \)` is not equal to a + b, so the given expression is not an identity.