Expand (x+25)(x-1): Multiplying Binomials with Square Numbers

In order to solve the following problem, simplify the expression step by step:

• Step 1: Compute $5^2$
  The first part of the expression involves $5^2$. We compute:
  $\quad 5^2 = 25$

• Step 2: Rewrite the expression
  Substitute $5^2$ with $25$ in the expression:
  $\quad (x + 25)(x - 1)$

• Step 3: Apply the FOIL method
  Expand the expression using the FOIL method:
  First: $x \cdot x = x^2$
  Outer: $x \cdot (-1) = -x$
  Inner: $25 \cdot x = 25x$
  Last: $25 \cdot (-1) = -25$

• Step 4: Combine like terms
  Combine all the terms:
  $\quad x^2 - x + 25x - 25$
  Combine $-x$ and $25x$:
  $\quad x^2 + 24x - 25$

Thus, the expanded expression is $x^2 + 24x - 25$.

Therefore, the final solution is:

$x^2 + 24x - 25$