Check please

Rewrite using distubutive property
3(x-2) 8(z-3) (t-4)5 -2(x-7)
3x-6 8z-24 5t-20 -2x+14

Correct!

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To rewrite the given expression using the distributive property, we need to apply the multiplication of each term inside the parentheses to every term outside the parentheses. Let's break it down step by step:

Given expression:
3(x-2) + 8(z-3) + (t-4)5 - 2(x-7)

Step 1: Distribute the coefficient 3 to each term inside the first set of parentheses: (x-2)
3 * x = 3x
3 * -2 = -6

Expression after distributing 3:
3x - 6 + 8(z-3) + (t-4)5 - 2(x-7)

Step 2: Distribute the coefficient 8 to each term inside the second set of parentheses: (z-3)
8 * z = 8z
8 * -3 = -24

Expression after distributing 8:
3x - 6 + 8z - 24 + (t-4)5 - 2(x-7)

Step 3: Distribute the coefficient 5 to each term inside the third set of parentheses: (t-4)
5 * t = 5t
5 * -4 = -20

Expression after distributing 5:
3x - 6 + 8z - 24 + 5t - 20 - 2(x-7)

Step 4: Distribute the coefficient -2 to each term inside the fourth set of parentheses: (x-7)
-2 * x = -2x
-2 * -7 = 14

Expression after distributing -2:
3x - 6 + 8z - 24 + 5t - 20 - 2x + 14

Step 5: Combine like terms:
(3x - 2x) = x
(-6 - 24) = -30
(-20 + 14) = -6

Final simplified expression using the distributive property:
x + 8z + 5t - 30 - 6

Therefore, the rewritten expression using the distributive property is:
x + 8z + 5t - 36