Question

multiply.
$(x - 5)(x^2 - 7x + 3)$
$(x - 5)(x^2 - 7x + 3) = \square$

Explanation:

Step1: Distribute \( x \)

Multiply \( x \) with each term in \( x^2 - 7x + 3 \):
\( x \cdot x^2 = x^3 \), \( x \cdot (-7x) = -7x^2 \), \( x \cdot 3 = 3x \).

Step2: Distribute \( -5 \)

Multiply \( -5 \) with each term in \( x^2 - 7x + 3 \):
\( -5 \cdot x^2 = -5x^2 \), \( -5 \cdot (-7x) = 35x \), \( -5 \cdot 3 = -15 \).

Step3: Combine like terms

Combine \( x^3 \), \( -7x^2 - 5x^2 \), \( 3x + 35x \), and \( -15 \):
\( x^3 + (-7x^2 - 5x^2) + (3x + 35x) - 15 = x^3 - 12x^2 + 38x - 15 \).

Answer:

\( x^3 - 12x^2 + 38x - 15 \)