write an expression equivalent to $4(2d + 10 - 5d)$.\n$4(2d + 10 - 5d)=d+?$
write an expression equivalent to $4(2d + 10 - 5d)$.\n$4(2d + 10 - 5d)=d+?$
Answer
Explanation:
Step1: Combine like terms inside the parentheses
First, combine (2d) and (-5d) in the expression (2d + 10-5d). Using the rule (a + b + c=a + c + b) (commutative property of addition), we have (2d-5d + 10=(2 - 5)d+10=-3d + 10). So the original expression (4(2d + 10-5d)) becomes (4(-3d + 10)).
Step2: Apply the distributive property
The distributive property is (a(b + c)=ab+ac). Here (a = 4), (b=-3d), and (c = 10). Then (4(-3d+10)=4\times(-3d)+4\times10). Calculating (4\times(-3d)=-12d) and (4\times10 = 40).
Answer:
(-12d + 40)