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]
