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Choose the expression that is equivalent to [tex]$15 w^2-\frac{4}{5}\left(5 w^2-15\right)+4 w$[/tex].

A. [tex]$11 w^2+4 w-12$[/tex]
B. [tex][tex]$11 w^2+4 w+12$[/tex][/tex]
C. [tex]$10 w^2+4 w-15$[/tex]
D. [tex]$10 w^2+4 w+15$[/tex]


Sagot :

To solve the expression [tex]\( 15 w^2 - \frac{4}{5}\left(5 w^2 - 15\right) + 4 w \)[/tex] for its equivalent form, follow these steps:

1. Expand the expression inside the parentheses:
[tex]\[ \frac{4}{5}\left(5 w^2 - 15\right) \][/tex]
Multiply both terms inside the parentheses by [tex]\(\frac{4}{5}\)[/tex]:
[tex]\[ \frac{4}{5} \cdot 5 w^2 - \frac{4}{5} \cdot 15 \][/tex]
This simplifies to:
[tex]\[ 4 w^2 - 12 \][/tex]

2. Substitute this result back into the original expression:
[tex]\[ 15 w^2 - (4 w^2 - 12) + 4 w \][/tex]
Expand to remove the parentheses:
[tex]\[ 15 w^2 - 4 w^2 + 12 + 4 w \][/tex]

3. Combine like terms:
Group the [tex]\(w^2\)[/tex] terms and the constant terms:
[tex]\[ (15 w^2 - 4 w^2) + 4 w + 12 \][/tex]
Simplify:
[tex]\[ 11 w^2 + 4 w + 12 \][/tex]

Therefore, the expression [tex]\(15 w^2 - \frac{4}{5}\left(5 w^2 - 15\right) + 4 w\)[/tex] is equivalent to [tex]\(\boxed{11 w^2 + 4 w + 12}\)[/tex].

So, the correct answer is:
B. [tex]\( 11 w^2 + 4 w + 12 \)[/tex]