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Which expression is equivalent to [tex]13 \sqrt{22b} - 10 \sqrt{22b}[/tex], if [tex]b \ \textgreater \ 0[/tex]?

A. [tex]23 \sqrt{226}[/tex]

B. [tex]130 \sqrt{22b}[/tex]

C. [tex]3 \sqrt{b^2}[/tex]

D. [tex]3 \sqrt{22b}[/tex]

Sagot :

GinnyAnswer
To determine an expression equivalent to [tex]\(13 \sqrt{22 b} - 10 \sqrt{22 b}\)[/tex], we will combine like terms.

1. First, note that both terms [tex]\(13 \sqrt{22 b}\)[/tex] and [tex]\(10 \sqrt{22 b}\)[/tex] have the common factor [tex]\(\sqrt{22 b}\)[/tex]:
[tex]\[ 13 \sqrt{22 b} - 10 \sqrt{22 b} \][/tex]

2. Factor out the common factor of [tex]\(\sqrt{22 b}\)[/tex]:
[tex]\[ (13 - 10) \sqrt{22 b} \][/tex]

3. Simplify the expression inside the parentheses:
[tex]\[ 3 \sqrt{22 b} \][/tex]

So, the expression [tex]\(13 \sqrt{22 b} - 10 \sqrt{22 b}\)[/tex] simplifies to [tex]\(3 \sqrt{22 b}\)[/tex].

Therefore, the correct answer is:
D. [tex]\(3 \sqrt{22 b}\)[/tex]
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