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Select the correct answer.

Which expression is equivalent to the given expression?

[tex]\[ 3x^2 + 5x - 7(x^2 + 4) \][/tex]

A. [tex]\[ x^2 + 28 \][/tex]

B. [tex]\[ -4x^2 + 5x - 28 \][/tex]

C. [tex]\[ x^2 + 4 \][/tex]

D. [tex]\[ -4x^2 + 5x - 4 \][/tex]

Sagot :

GinnyAnsweridn
Let's solve the given expression step-by-step and determine which option matches the simplified form of the expression:

Given expression:
[tex]\[ 3x^2 + 5x - 7(x^2 + 4) \][/tex]

First, let's expand the term [tex]\( -7(x^2 + 4) \)[/tex]:
[tex]\[ -7(x^2 + 4) = -7x^2 - 28 \][/tex]

Now, substitute this back into the original expression:
[tex]\[ 3x^2 + 5x - 7x^2 - 28 \][/tex]

Combine like terms:
[tex]\[ (3x^2 - 7x^2) + 5x - 28 \][/tex]
[tex]\[ -4x^2 + 5x - 28 \][/tex]

So, the simplified expression is:
[tex]\[ -4x^2 + 5x - 28 \][/tex]

Now, we compare this with the given options:

A. [tex]\( x^2 + 28 \)[/tex]
B. [tex]\( -4x^2 + 5x - 28 \)[/tex]
C. [tex]\( x^2 + 4 \)[/tex]
D. [tex]\( -4x^2 + 5x - 4 \)[/tex]

The correct expression that matches our simplified expression [tex]\( -4x^2 + 5x - 28 \)[/tex] is:

B. [tex]\( -4x^2 + 5x - 28 \)[/tex]

Therefore, the correct answer is 2.
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