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miv72 [106K]
3 years ago
11

Describe how to evaluate the expression 3^2 + (21 - 9) X 6÷2. Can someone help me out, please? I'm having trouble, and my teache

r isn't responding to my messages.
Mathematics
1 answer:
mylen [45]3 years ago
8 0

Answer:

3^2+\left(21-9\right)\times \:6\div \:2=45

Step-by-step explanation:

Given the expression

3^2\:+\:\left(21\:-\:9\right)\:\times \:6\div 2

Follow the PEMDAS order of operations

3^2\:+\:\left(21\:-\:9\right)\:\times \:6\div 2

calculate within parentheses  \:(21-9)=12

=3^2+12\times \:6\div \:2

calculate exponents  3^2=9

=9+12\times \:6\div \:2

Multiply and divide (left to right)

=9+36

Add and subtract (left to right)  12\times \:\:6\div \:\:2=36

=45

Thus,

3^2+\left(21-9\right)\times \:6\div \:2=45

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<h3>Distributive Property</h3>

The distributive property lets you group or ungroup terms using parentheses. It lets you multiply an external factor by every term in parentheses, expressing the result as a sum:

... a(b + c) = ab + ac . . . . . . factor <em>a</em> multiplies the terms <em>b</em> and <em>c</em>

and it lets you remove a common factor from different terms, putting that factor outside parentheses:

... ab + ac = a(b + c)

The letters <em>a</em>, <em>b</em>, <em>c</em> here can stand for any number or expression.

<h3>Homework</h3>

20. To do this problem, you need to eliminate the parentheses using the distributive property. Then, "collect terms," which is another application of the distributive property. The external factor outside the parentheses is (-2/3). Multiply that by each term in parentheses, and add the results.

After that, recognize that c is a factor of two of the terms. Add their coefficients to simplify that sum to one term.

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22. You are to evaluate the expression with x=2 two ways: as is, and after you simplify it by combining like terms.

<u>As is:</u>

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<u>Simplified:</u>

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I prefer simplifying the expression first. The number of calculations and chances for error are reduced.

23. It is convenient to check for equivalence after simplifying both expressions.

<u>First Expression:</u>

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<u>Second Expression:</u>

7x^2+7y +4x^2-4y=(7+4)x^2+(7-4)y=11x^2+3y

The simplified forms of the expressions are identical, so we conclude the expressions are equivalent.

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