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Chapter 3: Problem 66

Simplify. $$ (10+3 \cdot 4 \div 6)^{2}-11 \cdot 2^{2} \quad[1.9 \mathrm{c}] $$

Short Answer

Expert verified
(4+6)=10z\to2

Step by step solution

01

Simplify the expression inside the parentheses

First, simplify the expression inside the parentheses: take the terms inside the parentheses: $$(10+3 \times 4 \times 6)$$ Start by evaluating the multiplication and division from left to right inside the parentheses.
02

Perform multiplication and division within the parentheses

Evaluate multiplication and division from left to right. So, $$(3 \times 4 \times 6)$$ becomes the following: $$(3 \times 4 = 12)$$Next: $$(12 \times 6 = 2)$$. end result: $$10 \times 2 =12 ;$$.
03

Short Answer:

After solving, you will come up with the following short answer: Expression =x^;$$= x ;$$ $$.Concatenate the steps;$$ Answered final responses.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Order of Operations
When simplifying algebraic expressions, following the order of operations is crucial. The order of operations ensures that everyone calculates problems the same way and gets the same results. The mnemonic PEMDAS helps remember the order:
  • **P**arentheses
  • **E**xponents
  • **M**ultiplication and **D**ivision (from left to right)
  • **A**ddition and **S**ubtraction (from left to right)
Start inside the parentheses, then move to exponents, then perform multiplications and divisions from left to right. Finally, do any addition and subtraction from left to right. This standard process ensures accuracy.
Parentheses
Parentheses in algebra serve to group parts of an expression. They tell you which operations to complete first. Treat everything inside the parentheses as one entity鈥攊n other words, simplify it completely before doing anything outside of it. For the given exercise, the expression inside parentheses needs simplification first:
\( (10 + 3 \times 4 \times 6) \).
By following the order of operations inside these parentheses, you need to perform the multiplications and divisions before any addition.
Multiplication and Division
When both multiplication and division appear in an expression, handle them from left to right, according to their appearance. For the expression inside the parentheses:
\( 3 \times 4 \times 6 \), first evaluate the multiplication:
  • **Step 1**: \(3 \times 4 = 12\)
  • **Step 2**: \(12 \times 6 = 72\)
Now, the expression inside the parentheses is \(10 + 72\). Simplify this to get \(82\), then you can proceed with other operations outside the parentheses. Using multiplications and divisions correctly ensures the accuracy of your results.

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