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QuestionSimplify the following expressions using order of operations: a. (7+6)2=(7+6)^{2}= b. 72+62=7^{2}+6^{2}= c. 72+2⋅7⋅6+62=7^{2}+2 \cdot 7 \cdot 6+6^{2}=

Studdy Solution

STEP 1

Assumptions1. We are following the order of operations, which is Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). This is often remembered by the acronym PEMAS.

STEP 2

For part a, we first perform the operation inside the parentheses, which is addition.
(7+6)2=(13)2 (7+6)^{2} = (13)^{2}

STEP 3

Next, we perform the operation of exponentiation.
(13)2=169 (13)^{2} =169 So, (7+6)2=169(7+6)^{2}=169.

STEP 4

For part b, we first perform the operation of exponentiation for each term.
72+62=49+367^{2}+6^{2} =49 +36

STEP 5

Next, we perform the operation of addition.
49+36=8549 +36 =85 So, 72+2=857^{2}+^{2}=85.

STEP 6

For part c, we first perform the operation of exponentiation for each term and multiplication.
2+2⋅⋅6+62=49+2⋅⋅6+36^{2}+2 \cdot \cdot6+6^{2} =49 +2 \cdot \cdot6 +36

STEP 7

Next, we perform the operation of multiplication.
49+2⋅7⋅6+36=49+84+3649 +2 \cdot7 \cdot6 +36 =49 +84 +36

STEP 8

Finally, we perform the operation of addition.
49+84+36=16949 +84 +36 =169 So, 72+2⋅7⋅6+62=1697^{2}+2 \cdot7 \cdot6+6^{2}=169.

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