Question

Find the product. $$ (4 x+1)(x-8) $$

Short answer

The product of \( (4x + 1) \) and \( (x - 8) \) is \( 4x^2 - 31x - 8 \)

Step-by-step solution

Apply the distributive law

To find the product of the two binomial expressions, we need to multiply each term in the first binomial with each term in the second binomial. Using the distributive law (commonly remembered as the FOIL method - First, Outer, Inner, Last), we have: \( (4x + 1)(x - 8) = 4x \cdot x - 4x \cdot 8 + 1 \cdot x - 1 \cdot 8 \)

Multiply the terms

Perform the multiplication for each terms.So it becomes:= \( 4x^2 - 32x + x - 8 \)

Combine like terms

The final step in this problem is to combine the like terms. The like terms here are the terms with x, which are -32x and x. So, we add -32x and x together.This will give:= \( 4x^2 - 31x - 8 \)