(49p^2-7p+1)(7p+1)

Answer 1

To multiply the two expressions \((49p^2-7p+1)(7p+1)\), we can apply the distributive property (also known as the FOIL method for binomials).

1. Distribute \(7p\) to each term in \(49p^2 - 7p + 1\): \[ 7p \cdot 49p^2 = 343p^3 \] \[ 7p \cdot (-7p) = -49p^2 \] \[ 7p \cdot 1 = 7p \]

2. Next, distribute \(1\) to each term in \(49p^2 - 7p + 1\): \[ 1 \cdot 49p^2 = 49p^2 \] \[ 1 \cdot (-7p) = -7p \] \[ 1 \cdot 1 = 1 \]

3. Now combine all the products: \[ 343p^3 - 49p^2 + 7p + 49p^2 - 7p + 1 \]

4. Combine like terms:

   • The \(p^2\) terms: \(-49p^2 + 49p^2 = 0\)
   • The \(p\) terms: \(7p - 7p = 0\)
   • The constant: \(1\) remains as it is.

So the final result is: \[ 343p^3 + 1 \]

Thus, the product of \((49p^2-7p+1)(7p+1)\) is: \[ \boxed{343p^3 + 1} \]