If 2x + y = 6 and m - n = 2, what is the value of (4x + 2y) (4m - 4n)

96

Step-by-step explanation:

(4x + 2y) (4m - 4n) = ?

We have an equation

2x+y = 6

Multiply it by 2

2 (2x+y) = 2*6

Distribute

4x+2y = 12

Substitute 12 in for 4x+2y into the original problem

12 (4m - 4n) = ?

We have an equation

m-n = 2

Multiply this by 4

4 (m-n) = 4*2

Distribute

4m-4n = 8

Substitute 8 in for 4m - 4n in 12 (4m - 4n) = ?

12 * 8 = ?

96

96

Step-by-step explanation:

If m - n = 2, then 4m - 4n = 4 (m - n) = 4 (2).

Then (4x + 2y) (4m - 4n) equals (4x + 2y) (8), or 8 (4x + 2y).

But we are told that 2x + y = 6. Multiplying all terms by 2, we get

4x + 2y = 12. Substituting 12 for 4x + 2y, we get our final answer:

(4x + 2y) (4m - 4n) equals (4x + 2y) (8), or 8 (4x + 2y), or 8 (12) = 96