The expression 64a3−b3
 can be factored as:

Question 5Select one:

(4a−b)3


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(4a+b)(16a2+4ab+b2)


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(4a−b)(16a2−4ab−b2)


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does not factor at all

cross out

none of these

The given expression is \( 64a^3 - b^3 \). This is a difference of cubes, which can be factored using the identity:

\[
x^3 - y^3 = (x - y)(x^2 + xy + y^2)
\]

Here, \( x = 4a \) and \( y = b \), because \( 64a^3 = (4a)^3 \).

Applying the formula:

\[
64a^3 - b^3 = (4a - b)((4a)^2 + (4a)(b) + b^2)
\]

Simplifying the second factor:

\[
(4a)^2 + (4a)(b) + b^2 = 16a^2 + 4ab + b^2
\]

Thus, the factored form of \( 64a^3 - b^3 \) is:

\[
(4a - b)(16a^2 + 4ab + b^2)
\]

The correct answer is: 

\[
\boxed{(4a - b)(16a^2 + 4ab + b^2)}
\]

Let me know if you'd like more details or have any questions!

Here are 5 related questions:
1. How do you factor the sum of cubes?
2. Can the expression \( a^3 + b^3 \) be factored similarly?
3. How do you recognize when an expression is a difference of cubes?
4. What is the general formula for factoring the difference of squares?
5. Can you apply this same method to \( 8x^3 - 27y^3 \)?

**Tip:** When factoring cubes, always look for patterns like perfect cubes and apply the appropriate identity.

The expression 64a^3 − b^3 can be factored as: (4a−b)(16a^2+4ab+b^2)

Learn how to factor the expression 64a^3 - b^3 using the difference of cubes formula. This solution explains how to apply the formula and break down the expression into (4a - b)(16a^2 + 4ab + b^2). Ideal for high school students studying algebra.

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