Use the distributive property to expand
38(−8−2�)\frac{3}{8}\left(-8-2y\right)
8
3
(−8−2y)
To expand the given expression using the distributive property, we need to distribute 38 across the terms inside the parentheses:
38(-8) + 38(-2/8)(-8) + 38(-2/8)(-2y)
=-304 + (38 * -2/8 * -8) + (38 * -2/8 * -2y)
=-304 + (76 * -8) + (19 * -2y)
=-304 + (-608) + (-38y)
= -912 - 38y
Use the distributive property to expand 3/8 (-8 - 2y)
To expand the expression 3/8(-8 - 2y) using the distributive property, we need to distribute the fraction 3/8 across the terms inside the parentheses:
3/8(-8) + 3/8(-2y)
= (3 * -8) / 8 + (3 * -2y) / 8
= -24/8 - 6y/8
= -3 - (3/4)y
So, 3/8(-8 - 2y) expands to -3 - (3/4)y.
To use the distributive property to expand the expression 38(−8−2/3) * (3/8)(−8−2y), we need to distribute the 38 to both terms inside the parentheses, and then distribute the (3/8) to both terms inside the second set of parentheses. Let's go step by step:
Step 1: Distribute 38 to both terms inside the first set of parentheses:
38 * (-8) + 38 * (-2/3)
Step 2: Simplify the multiplication:
-304 + (-76/3)
Step 3: Find a common denominator for -304 and -76/3:
To add fractions, we need a common denominator. The denominator of -304 is 1, and the denominator of -76/3 is 3. The least common denominator is 3, so let's rewrite -304 with denominator 3:
-304/1 = -304/1 * 3/3 = -912/3
Step 4: Add the fractions:
-912/3 + (-76/3) = -988/3
Now, let's continue with the second set of parentheses:
Step 5: Distribute (3/8) to both terms inside the second set of parentheses:
(3/8) * (-8) + (3/8) * (-2y)
Step 6: Simplify the multiplication:
-24/8 + (-6y/8) = -24/8 - 6y/8
Step 7: Combine the fractions:
(-24 - 6y)/8
So, the expanded expression is (-988/3) * ((-24 - 6y)/8).
To expand the expression using the distributive property, we need to multiply every term inside the parentheses with the term outside of the parentheses.
Let's start by multiplying the first term inside the parentheses with the term outside the parentheses:
38 * (-8) = -304
Next, multiply the second term inside the parentheses with the term outside the parentheses:
38 * (-2/8) = -76/8 = -19/2
Now, we have:
-304 - 19/2(8 - 2y)
To simplify the remaining expression, we can apply the distributive property again.
Multiply -19/2 with 8:
-19/2 * 8 = -152/2 = -76
Multiply -19/2 with -2y:
-19/2 * -2y = 19y/2
So, the expanded expression is:
-304 - 76 + 19y/2
Combine like terms:
-304 - 76 = -380
The final expanded expression is:
-380 + 19y/2