Question

Find the product:

(x + 3) (x + 5) (x + 7)

Answer 1

Given: (x + 3)(x + 5)(x + 7)

Step-wise calculation:

1. First, multiply the first two binomials:

(x + 3)(x + 5) = x² + 5x + 3x + 15

(x + 3)(x + 5) = x² + 8x + 15

2. Now multiply this result with the third binomial (x + 7): 

(x² + 8x + 15)(x + 7)

3. Distribute each term in the trinomial by (x) and then by (7):

= (x²)(x) + (8x)(x) + 15(x) + (x²)(7) + (8x)(7) + 15(7)

= x³ + 8x² + 15x + 7x² + 56x + 105

4. Combine like terms:

x³ + (8x² + 7x²) + (15x + 56x) + 105 

= x³ + 15x² + 71x + 105