Math Snap

STEP 1

1. We are given an expression that involves two binomials and a constant factor.
2. The goal is to expand the expression by applying the distributive property (also known as the FOIL method for binomials).

STEP 2

1. Apply the distributive property to expand the product of the binomials.
2. Multiply the expanded expression by the constant factor.

STEP 3

Apply the distributive property to expand the product of the binomials $(12x - y)(2x - 7y)$.
- First, multiply the first terms: $12x \times 2x = 24x^2$.
- Next, multiply the outer terms: $12x \times (-7y) = -84xy$.
- Then, multiply the inner terms: $-y \times 2x = -2xy$.
- Finally, multiply the last terms: $-y \times (-7y) = 7y^2$.
Combine these results:
$$24x^2 - 84xy - 2xy + 7y^2$$

STEP 4

Combine like terms in the expanded expression:
$$24x^2 - 86xy + 7y^2$$

Multiply the entire expanded expression by the constant factor $3$:
$$3(24x^2 - 86xy + 7y^2)$$ Distribute the $3$ to each term:
$$72x^2 - 258xy + 21y^2$$ The expanded expression is:
$$\boxed{72x^2 - 258xy + 21y^2}$$