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Answer :
To simplify the expression [tex]\(7x^2(6x + 3x^2 - 4)\)[/tex], we'll distribute [tex]\(7x^2\)[/tex] to each term inside the parentheses. Here’s how we do it step-by-step:
1. Distribute [tex]\(7x^2\)[/tex] to [tex]\(6x\)[/tex]:
- Multiply the coefficients: [tex]\(7 \times 6 = 42\)[/tex]
- Multiply the variables: [tex]\(x^2 \times x = x^3\)[/tex]
- So, [tex]\(7x^2 \times 6x = 42x^3\)[/tex].
2. Distribute [tex]\(7x^2\)[/tex] to [tex]\(3x^2\)[/tex]:
- Multiply the coefficients: [tex]\(7 \times 3 = 21\)[/tex]
- Multiply the variables: [tex]\(x^2 \times x^2 = x^4\)[/tex]
- So, [tex]\(7x^2 \times 3x^2 = 21x^4\)[/tex].
3. Distribute [tex]\(7x^2\)[/tex] to [tex]\(-4\)[/tex]:
- Multiply the coefficients: [tex]\(7 \times -4 = -28\)[/tex]
- The variable remains: [tex]\(x^2\)[/tex]
- So, [tex]\(7x^2 \times -4 = -28x^2\)[/tex].
Now, combine all these results together:
- [tex]\(21x^4 + 42x^3 - 28x^2\)[/tex]
So, the simplified expression is [tex]\(21x^4 + 42x^3 - 28x^2\)[/tex].
Therefore, the correct simplification choice is:
[tex]\[21x^4 + 42x^3 - 28x^2\][/tex]
1. Distribute [tex]\(7x^2\)[/tex] to [tex]\(6x\)[/tex]:
- Multiply the coefficients: [tex]\(7 \times 6 = 42\)[/tex]
- Multiply the variables: [tex]\(x^2 \times x = x^3\)[/tex]
- So, [tex]\(7x^2 \times 6x = 42x^3\)[/tex].
2. Distribute [tex]\(7x^2\)[/tex] to [tex]\(3x^2\)[/tex]:
- Multiply the coefficients: [tex]\(7 \times 3 = 21\)[/tex]
- Multiply the variables: [tex]\(x^2 \times x^2 = x^4\)[/tex]
- So, [tex]\(7x^2 \times 3x^2 = 21x^4\)[/tex].
3. Distribute [tex]\(7x^2\)[/tex] to [tex]\(-4\)[/tex]:
- Multiply the coefficients: [tex]\(7 \times -4 = -28\)[/tex]
- The variable remains: [tex]\(x^2\)[/tex]
- So, [tex]\(7x^2 \times -4 = -28x^2\)[/tex].
Now, combine all these results together:
- [tex]\(21x^4 + 42x^3 - 28x^2\)[/tex]
So, the simplified expression is [tex]\(21x^4 + 42x^3 - 28x^2\)[/tex].
Therefore, the correct simplification choice is:
[tex]\[21x^4 + 42x^3 - 28x^2\][/tex]
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