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Answer :
To solve the problem, let's simplify the given expression step-by-step:
The expression we start with is:
[tex]\[ -4x^3 - 12x^3 + 9x^2 \][/tex]
1. Combine Like Terms:
- Notice that [tex]\(-4x^3\)[/tex] and [tex]\(-12x^3\)[/tex] are like terms because they both contain [tex]\(x^3\)[/tex].
- To combine these, add their coefficients: [tex]\(-4 + (-12) = -16\)[/tex].
- So, [tex]\(-4x^3 - 12x^3 = -16x^3\)[/tex].
2. Write the Simplified Expression:
- Now, put the combined term and the [tex]\(9x^2\)[/tex] together:
[tex]\[ -16x^3 + 9x^2 \][/tex]
From the choices given, the expression [tex]\(-16x^3 + 9x^2\)[/tex] matches the third option: [tex]\(-16 x^3 + 9 x^2\)[/tex].
So, the expression equivalent to [tex]\(-4x^3 - 12x^3 + 9x^2\)[/tex] is [tex]\(-16x^3 + 9x^2\)[/tex].
The expression we start with is:
[tex]\[ -4x^3 - 12x^3 + 9x^2 \][/tex]
1. Combine Like Terms:
- Notice that [tex]\(-4x^3\)[/tex] and [tex]\(-12x^3\)[/tex] are like terms because they both contain [tex]\(x^3\)[/tex].
- To combine these, add their coefficients: [tex]\(-4 + (-12) = -16\)[/tex].
- So, [tex]\(-4x^3 - 12x^3 = -16x^3\)[/tex].
2. Write the Simplified Expression:
- Now, put the combined term and the [tex]\(9x^2\)[/tex] together:
[tex]\[ -16x^3 + 9x^2 \][/tex]
From the choices given, the expression [tex]\(-16x^3 + 9x^2\)[/tex] matches the third option: [tex]\(-16 x^3 + 9 x^2\)[/tex].
So, the expression equivalent to [tex]\(-4x^3 - 12x^3 + 9x^2\)[/tex] is [tex]\(-16x^3 + 9x^2\)[/tex].
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