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Explain how to write an equivalent expression using the distributive property:

[tex]\[ 2(11 + y) \][/tex]

Sagot :

GinnyAnswer
Certainly! Let's solve the expression [tex]\( 2(11 + y) \)[/tex] using the distributive property. The distributive property states that for any three numbers [tex]\( a \)[/tex], [tex]\( b \)[/tex], and [tex]\( c \)[/tex]:

[tex]\[ a(b + c) = ab + ac \][/tex]

Now let's apply this property step-by-step to our problem:

1. Identify the terms inside the parentheses: Here, we have [tex]\( 11 \)[/tex] and [tex]\( y \)[/tex] inside the parentheses.

2. Multiply each term inside the parentheses by the number outside the parentheses: In this case, the number outside the parentheses is [tex]\( 2 \)[/tex].

- First, multiply [tex]\( 2 \)[/tex] by [tex]\( 11 \)[/tex]:
[tex]\[ 2 \times 11 = 22 \][/tex]

- Then, multiply [tex]\( 2 \)[/tex] by [tex]\( y \)[/tex]:
[tex]\[ 2 \times y = 2y \][/tex]

3. Combine the results: According to the distributive property, combine these products together to form the equivalent expression:
[tex]\[ 22 + 2y \][/tex]

So, the expression [tex]\( 2(11 + y) \)[/tex] is equivalent to [tex]\( 22 + 2y \)[/tex].

Therefore, the simplified and equivalent expression is:
[tex]\[ 22 + 2y \][/tex]
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