Evaluate (7+2+3)(7+6)(12-3-4): Multi-Parentheses Multiplication

Question

(7+2+3)(7+6)(1234)=? (7+2+3)(7+6)(12-3-4)=\text{?}

Video Solution

Solution Steps

00:00 Solve
00:03 Always solve parentheses first, and the leftmost operation first
00:13 We'll continue to solve all parentheses using the same method
00:16 There's multiplication between parentheses
00:23 We'll continue to solve all parentheses
00:38 We'll arrange the equation so it's easier to solve
00:47 We'll solve each multiplication separately and then continue solving
00:51 We'll solve using long multiplication
01:42 And this is the solution to the question

Step-by-Step Solution

Let's simplify this expression while following the order of operations which states that exponents come before multiplication and division, which come before addition and subtraction, and that parentheses come before all of these,

therefore we'll start by simplifying the expressions in parentheses first:
(7+2+3)(7+6)(1234)=12135 (7+2+3)(7+6)(12-3-4)=\\ 12\cdot13\cdot5

Now we'll calculate the multiplication result step by step from left to right:

12135=1565=780 12\cdot13\cdot5 =\\ 156\cdot5 =\\ 780

Note that since the commutative property of multiplication applies to the expression we simplified above between all terms, the order of operations in this calculation doesn't matter (it's not necessary to perform the left multiplication first etc. as we did), however it is recommended to practice performing operations from left to right since this is the natural order of arithmetic operations (in the absence of parentheses, or other preceding arithmetic operations according to the order of operations mentioned at the beginning of this solution)

Therefore the correct answer is answer C.

Answer

780