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Answer :
To simplify the expression [tex]\(9x^2(4x + 2x^2 - 1)\)[/tex], we'll distribute [tex]\(9x^2\)[/tex] across each term inside the parentheses. Let's go through this step-by-step:
1. Distribute [tex]\(9x^2\)[/tex] to [tex]\(4x\)[/tex]:
Multiply the coefficients and add the exponents of [tex]\(x\)[/tex]:
[tex]\[
9x^2 \cdot 4x = 36x^{2+1} = 36x^3
\][/tex]
2. Distribute [tex]\(9x^2\)[/tex] to [tex]\(2x^2\)[/tex]:
Again, multiply the coefficients and add the exponents of [tex]\(x\)[/tex]:
[tex]\[
9x^2 \cdot 2x^2 = 18x^{2+2} = 18x^4
\][/tex]
3. Distribute [tex]\(9x^2\)[/tex] to [tex]\(-1\)[/tex]:
Simply multiply the coefficients, as there are no exponents of [tex]\(x\)[/tex] to worry about:
[tex]\[
9x^2 \cdot (-1) = -9x^2
\][/tex]
4. Combine all the terms:
Now, put all the resulting terms together to form the simplified expression:
[tex]\[
18x^4 + 36x^3 - 9x^2
\][/tex]
Therefore, the correct simplification of the expression [tex]\(9x^2(4x + 2x^2 - 1)\)[/tex] is:
[tex]\[
18x^4 + 36x^3 - 9x^2
\][/tex]
1. Distribute [tex]\(9x^2\)[/tex] to [tex]\(4x\)[/tex]:
Multiply the coefficients and add the exponents of [tex]\(x\)[/tex]:
[tex]\[
9x^2 \cdot 4x = 36x^{2+1} = 36x^3
\][/tex]
2. Distribute [tex]\(9x^2\)[/tex] to [tex]\(2x^2\)[/tex]:
Again, multiply the coefficients and add the exponents of [tex]\(x\)[/tex]:
[tex]\[
9x^2 \cdot 2x^2 = 18x^{2+2} = 18x^4
\][/tex]
3. Distribute [tex]\(9x^2\)[/tex] to [tex]\(-1\)[/tex]:
Simply multiply the coefficients, as there are no exponents of [tex]\(x\)[/tex] to worry about:
[tex]\[
9x^2 \cdot (-1) = -9x^2
\][/tex]
4. Combine all the terms:
Now, put all the resulting terms together to form the simplified expression:
[tex]\[
18x^4 + 36x^3 - 9x^2
\][/tex]
Therefore, the correct simplification of the expression [tex]\(9x^2(4x + 2x^2 - 1)\)[/tex] is:
[tex]\[
18x^4 + 36x^3 - 9x^2
\][/tex]
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