Questionpicy (Max 100\%) $3(12 x-y)(2 x-7 y)$

Studdy Solution

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:
$24x^2 - 86xy + 7y^2$

STEP 5

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:
$\boxed{72x^2 - 258xy + 21y^2}$

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