Simplify 5h-3[4k-6m+2{3h-(2h+3k)}]
5 h - 3[4k-6m+2h-6k]
5 h - 12 k + 18 m -6 h +18 k
- h + 6 k + 18 m
To simplify the given expression, we need to apply the order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction), which dictates the order in which operations should be performed.
Let's break down the given expression step by step:
1. Start by simplifying the innermost parentheses. Inside the curly braces ({ }), we have:
3h - (2h + 3k)
Remove the parentheses and distribute the negative sign inside:
3h - 2h - 3k
Combine like terms:
(3h - 2h) - 3k
h - 3k
2. Now, substitute this simplified expression back into the original expression:
5h - 3[4k - 6m + 2(h - 3k)]
3. Continue simplifying by multiplying each term within the square brackets by the coefficient 3:
5h - 3 * 4k + 3 * 6m + 3 * 2(h - 3k)
Simplify further:
5h - 12k + 18m + 6(h - 3k)
4. Distribute the coefficient 6 inside the parentheses:
5h - 12k + 18m + 6h - 6 * 3k
Simplify further:
5h - 12k + 18m + 6h - 18k
5. Finally, combine the like terms:
(5h + 6h) + (-12k - 18k) + 18m
Combine like terms for h and k:
11h - 30k + 18m
So, the simplified form of the expression 5h - 3[4k - 6m + 2{3h - (2h + 3k)}] is 11h - 30k + 18m.