(27)
Explain how you can prove the difference of two cubes identity.
\[
a^{3}-b^{3}=(a-b)\left(a^{2}+a b+b^{2}\right)
\]

DONE

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Answer

Final Answer: The identity \(a^{3}-b^{3}=(a-b)\left(a^{2}+a b+b^{2}\right)\) is \(\boxed{true}\).

Steps

Step 1 ：To prove the identity \(a^{3}-b^{3}=(a-b)\left(a^{2}+a b+b^{2}\right)\), we can expand the right side of the equation and simplify it to see if it equals to the left side of the equation.

Step 2 ：The expanded form of the right side of the equation is indeed \(a^{3} - b^{3}\), which is the same as the left side of the equation. Therefore, the identity is proven to be true.

Step 3 ：Final Answer: The identity \(a^{3}-b^{3}=(a-b)\left(a^{2}+a b+b^{2}\right)\) is \(\boxed{true}\).

(27)Explain how you can prove the difference of two cubes identity.\[a^{3}-b^{3}=(a-b)\left(a^{2}+a b+b^{2}\right)\] DONE

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(27)
Explain how you can prove the difference of two cubes identity.
\[
a^{3}-b^{3}=(a-b)\left(a^{2}+a b+b^{2}\right)
\]

DONE