The algorithm shown executes to evaluate which algebraic expression?

The algorithm shown executes to evaluate which algebraic expression?

• A. (8k+3)^3
• B. 8(k+3)^3
• C. 8^3(k+3)
• D. 8^3(k+3)^3

Answer: (D)

The correct answer is associated with the algebraic expression \( 8^3(k+3)^3 \) because the algorithm likely follows the structure of the binomial expansion. In binomial expansion, particularly using the binomial theorem, when evaluating an expression of the form \( (a + b)^n \), where \( a \) and \( b \) are terms and \( n \) is a positive integer, the result is a sum of terms that involve powers of \( a \) and \( b \) multiplied by binomial coefficients. When evaluating \( (k+3)^3 \), the expansion will yield terms including \( k^3 \), \( 3k^2 \cdot 3 \), \( 3k \cdot 9 \), and \( 27 \). Each of these terms is multiplied by \( 8^3 \), hence the expression takes on the form \( 8^3(k+3)^3 \). Since \( 8 \) can be viewed as \( 2^3 \) and \( 8^3 \) simplifies to \( 2^9 \), the presence of the cube from \( (k+3) \) aligns with the

The correct answer is associated with the algebraic expression ( 8^3(k+3)^3 ) because the algorithm likely follows the structure of the binomial expansion.

In binomial expansion, particularly using the binomial theorem, when evaluating an expression of the form ( (a + b)^n ), where ( a ) and ( b ) are terms and ( n ) is a positive integer, the result is a sum of terms that involve powers of ( a ) and ( b ) multiplied by binomial coefficients.

When evaluating ( (k+3)^3 ), the expansion will yield terms including ( k^3 ), ( 3k^2 \cdot 3 ), ( 3k \cdot 9 ), and ( 27 ). Each of these terms is multiplied by ( 8^3 ), hence the expression takes on the form ( 8^3(k+3)^3 ).

Since ( 8 ) can be viewed as ( 2^3 ) and ( 8^3 ) simplifies to ( 2^9 ), the presence of the cube from ( (k+3) ) aligns with the