Answer :
Sure! Let's simplify the expression step by step.
We are given the expression:
[tex]\[ 6x^3y^2(4x^4 - 3xy) \][/tex]
Step 1: Apply the Distributive Property.
We'll distribute [tex]\(6x^3y^2\)[/tex] into each term inside the parenthesis.
[tex]\[ 6x^3y^2 \times 4x^4 - 6x^3y^2 \times 3xy \][/tex]
Step 2: Multiply each term.
- For the first term, [tex]\(6x^3y^2 \times 4x^4\)[/tex]:
- Coefficients: [tex]\(6 \times 4 = 24\)[/tex]
- [tex]\(x\)[/tex] terms: [tex]\(x^3 \times x^4 = x^{3+4} = x^7\)[/tex]
- [tex]\(y^2\)[/tex] remains the same, so the term is [tex]\(24x^7y^2\)[/tex].
- For the second term, [tex]\(6x^3y^2 \times 3xy\)[/tex]:
- Coefficients: [tex]\(6 \times 3 = 18\)[/tex]
- [tex]\(x\)[/tex] terms: [tex]\(x^3 \times x = x^{3+1} = x^4\)[/tex]
- [tex]\(y\)[/tex] terms: [tex]\(y^2 \times y = y^{2+1} = y^3\)[/tex]
- Thus, the term is [tex]\(18x^4y^3\)[/tex].
Step 3: Write the simplified expression.
Subtract the second term from the first term:
[tex]\[ 24x^7y^2 - 18x^4y^3 \][/tex]
Out of the provided options, this matches the first choice:
[tex]\[ 24x^7y^2 - 18x^4y^3 \][/tex]
So the simplified expression is:
[tex]\[ 24x^7y^2 - 18x^4y^3 \][/tex]
And the corresponding option is 1.
We are given the expression:
[tex]\[ 6x^3y^2(4x^4 - 3xy) \][/tex]
Step 1: Apply the Distributive Property.
We'll distribute [tex]\(6x^3y^2\)[/tex] into each term inside the parenthesis.
[tex]\[ 6x^3y^2 \times 4x^4 - 6x^3y^2 \times 3xy \][/tex]
Step 2: Multiply each term.
- For the first term, [tex]\(6x^3y^2 \times 4x^4\)[/tex]:
- Coefficients: [tex]\(6 \times 4 = 24\)[/tex]
- [tex]\(x\)[/tex] terms: [tex]\(x^3 \times x^4 = x^{3+4} = x^7\)[/tex]
- [tex]\(y^2\)[/tex] remains the same, so the term is [tex]\(24x^7y^2\)[/tex].
- For the second term, [tex]\(6x^3y^2 \times 3xy\)[/tex]:
- Coefficients: [tex]\(6 \times 3 = 18\)[/tex]
- [tex]\(x\)[/tex] terms: [tex]\(x^3 \times x = x^{3+1} = x^4\)[/tex]
- [tex]\(y\)[/tex] terms: [tex]\(y^2 \times y = y^{2+1} = y^3\)[/tex]
- Thus, the term is [tex]\(18x^4y^3\)[/tex].
Step 3: Write the simplified expression.
Subtract the second term from the first term:
[tex]\[ 24x^7y^2 - 18x^4y^3 \][/tex]
Out of the provided options, this matches the first choice:
[tex]\[ 24x^7y^2 - 18x^4y^3 \][/tex]
So the simplified expression is:
[tex]\[ 24x^7y^2 - 18x^4y^3 \][/tex]
And the corresponding option is 1.
