What is the product of the polynomials below? \( (8 x+8)(x+3) \) A. \( 8 x^{2}+34 x+64 \) B. \( 8 x^{2}+16 x+32 \) C. \( 8 x^{2}+32 x+24 \) D. \( 8 x^{2}+11 x+16 \)

To find the product of the polynomials \( (8x + 8)(x + 3) \), we can use the distributive property (also called the FOIL method for binomials): 1. Multiply the first terms: \( 8x * x = 8x^2 \) 2. Multiply the outer terms: \( 8x * 3 = 24x \) 3. Multiply the inner terms: \( 8 * x = 8x \) 4. Multiply the last terms: \( 8 * 3 = 24 \) Now, combine all the terms: \( 8x^2 + 24x + 8x + 24 \) which simplifies to \( 8x^2 + 32x + 24 \). So the answer is \( 8x^2 + 32x + 24 \), which corresponds to option C. If you were in an algebra class and wanted to break it down, you'd probably enjoy using colorful markers to visually represent each step. This way, each part of the expansion stands out, making it easier to see how they all come together in the end! For those looking to deepen their understanding, consider practicing polynomial multiplication with varied degree terms. Try using different combinations of coefficients and constants; it’s like cooking—experimenting might lead you to create something truly delicious in the realm of math!