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scZoUnD [109]
1 year ago
8

Name the property used in each step.

Mathematics
1 answer:
jarptica [38.1K]1 year ago
5 0

Answer:

\begin{aligned}ab(a+b) & = (ab)a+(ab)b & & \textsf{Distributive Property of Addition} \\& = a(ab)+(ab)b & & \textsf{Commutative Property of Multiplication} \\& = (a \cdot a)b + a(b \cdot b) & & \textsf{Associative Property of Multiplication}\\& = a^2b+ab^2 & & \textsf{Property of Exponents}\end{aligned}

Step-by-step explanation:

<u>Distributive Property of Addition</u>

Multiplying a number by a group of numbers added together is the same as multiplying each number separately.

Addition: a(b + c) = ab + ac

Subtraction: a(b - c) = ab – ac

<u>Commutative Property</u>

Changing the order or position of two numbers does not change the end result.

Applies to <u>addition</u> and <u>multiplication</u> only.

Addition: a + b = b + a

Multiplication: a × b = b × a

<u>Associative Property</u>

Grouping of numbers by parentheses in a different way does not affect their sum or product.

Applies to <u>addition</u> and <u>multiplication</u> only.

Addition: (a + b) + c = a + (b + c) = (a + c) + b

Multiplication: (a × b) × c = a × (b × c) = (a × c) × b

<u>Property of Exponents</u>

The <u>exponent</u> of a number shows how many times it should be <u>multiplied by itself</u>.

a × a × a = a³

b × b × b × b = b⁴

\begin{aligned}ab(a+b) & = (ab)a+(ab)b & & \textsf{Distributive Property of Addition} \\& = a(ab)+(ab)b & & \textsf{Commutative Property of Multiplication} \\& = (a \cdot a)b + a(b \cdot b) & & \textsf{Associative Property of Multiplication}\\& = a^2b+ab^2 & & \textsf{Property of Exponents}\end{aligned}

Learn more about Property Laws here:

brainly.com/question/28210762

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